trigonometry.scad
Trigonometry shortcuts for people who can't be bothered to remember all the function relations, or silly acronyms like SOHCAHTOA.
To use, add the following lines to the beginning of your file:
include <BOSL2/std.scad>
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Section: General Triangle Functions
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law_of_cosines()– Applies the Law of Cosines for an arbitrary triangle. -
law_of_sines()– Applies the Law of Sines for an arbitrary triangle.
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Section: Right Triangle Functions
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hyp_opp_to_adj()– Returns the adjacent side length from the lengths of the hypotenuse and the opposite side. -
opp_hyp_to_adj()– Returns the adjacent side length from the lengths of the opposite side and the hypotenuse. -
hyp_ang_to_adj()– Returns the adjacent side length from the length of the hypotenuse and the reference reference angle. -
ang_hyp_to_adj()– Returns the adjacent side length from the reference reference angle and the length of the hypotenuse. -
opp_ang_to_adj()– Returns the adjacent side length from the length of the opposite side and the reference reference angle. -
ang_opp_to_adj()– Returns the adjacent side length from the reference reference angle and the length of the opposite side. -
hyp_adj_to_opp()– Returns the opposite side length from the lengths of the hypotenuse and the adjacent side. -
adj_hyp_to_opp()– Returns the opposite side length from the lengths of the adjacent side and the hypotenuse. -
hyp_ang_to_opp()– Returns the opposite side length from the length of the hypotenuse and the reference reference angle. -
ang_hyp_to_opp()– Returns the opposite side length from the reference reference angle and the length of the hypotenuse. -
adj_ang_to_opp()– Returns the opposite side length from the length of the adjacent side and the reference reference angle. -
ang_adj_to_opp()– Returns the opposite side length from the reference reference angle and the length of the adjacent side. -
adj_opp_to_hyp()– Returns the hypotenuse length from the lengths of the adjacent and opposite sides. -
opp_adj_to_hyp()– Returns the hypotenuse length from the lengths of the opposite and adjacent sides. -
adj_ang_to_hyp()– Returns the hypotenuse length from the length of the adjacent side and the reference reference angle. -
ang_adj_to_hyp()– Returns the hypotenuse length from the reference reference angle and length of the adjacent side. -
opp_ang_to_hyp()– Returns the hypotenuse length from the length of the opposite side and the reference reference angle. -
ang_opp_to_hyp()– Returns the hypotenuse length from the reference reference angle and the length of the opposite side. -
hyp_adj_to_ang()– Returns the reference reference angle from the lengths of the hypotenuse and the adjacent side. -
adj_hyp_to_ang()– Returns the reference angle from the lengths of the adjacent side and the hypotenuse. -
hyp_opp_to_ang()– Returns the reference reference angle from the lengths of the hypotenuse and the opposite side. -
opp_hyp_to_ang()– Returns the reference reference angle from the lengths of the opposite side and the hypotenuse. -
adj_opp_to_ang()– Returns the reference angle from the lengths of the adjacent and opposite sides. -
opp_adj_to_ang()– Returns the reference reference angle from the lengths of the opposite and adjacent sides.
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Synopsis: Applies the Law of Cosines for an arbitrary triangle.
Topics: Geometry, Trigonometry, Triangles
See Also: law_of_sines()
Usage:
- C = law_of_cosines(a, b, c);
- c = law_of_cosines(a, b, C=);
Description:
Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the reference angle in degrees for the corner opposite of the third side. Given two side lengths, and the reference angle between them, returns the length of the third side.
Figure 1.1.1:
Arguments:
| By Position | What it does |
|---|---|
a |
The length of the first side. |
b |
The length of the second side. |
c |
The length of the third side. |
| By Name | What it does |
|---|---|
C |
The reference angle in degrees of the corner opposite of the third side. |
Synopsis: Applies the Law of Sines for an arbitrary triangle.
Topics: Geometry, Trigonometry, Triangles
See Also: law_of_cosines()
Usage:
- B = law_of_sines(a, A, b);
- b = law_of_sines(a, A, B=);
Description:
Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the reference angle between them, returns the reference angle of the corner opposite of the second side. Given a side length, the opposing reference angle, and a second reference angle, returns the length of the side opposite of the second reference angle.
Figure 1.2.1:
Arguments:
| By Position | What it does |
|---|---|
a |
The length of the first side. |
A |
The reference angle in degrees of the corner opposite of the first side. |
b |
The length of the second side. |
| By Name | What it does |
|---|---|
B |
The reference angle in degrees of the corner opposite of the second side. |
This is a set of functions to make it easier to perform trig calculations on right triangles. In general, all these functions are named using these abbreviations:
- ang: The reference reference angle size in degrees.
- hyp: The length of the Hypotenuse.
- adj: The length of the side adjacent to the reference reference angle.
- opp: The length of the side opposite to the reference reference angle.
If you know two of those, and want to know the value of a third, you will need to call a
function named like AAA_BBB_to_CCC(). For example, if you know the length of the hypotenuse,
and the length of the side adjacent to the reference reference angle, and want to learn the length of the side
opposite to the reference reference angle, you will call opp = hyp_adj_to_opp(hyp,adj);.
Figure 2.1:
Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- adj = hyp_opp_to_adj(hyp,opp);
Description:
Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
adj = hyp_opp_to_adj(5,3); // Returns: 4
Synopsis: Returns the adjacent side length from the lengths of the opposite side and the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- adj = opp_hyp_to_adj(opp,hyp);
Description:
Given the lengths of the opposite side and hypotenuse of a right triangle, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
adj = opp_hyp_to_adj(3,5); // Returns: 4
Synopsis: Returns the adjacent side length from the length of the hypotenuse and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- adj = hyp_ang_to_adj(hyp,ang);
Description:
Given the length of the hypotenuse and the reference reference angle of a right triangle, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
adj = hyp_ang_to_adj(8,60); // Returns: 4
Synopsis: Returns the adjacent side length from the reference reference angle and the length of the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- adj = ang_hyp_to_adj(ang,hyp);
Description:
Given the reference reference angle and the length of the hypotenuse of a right triangle, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
adj = ang_hyp_to_adj(60,8); // Returns: 4
Synopsis: Returns the adjacent side length from the length of the opposite side and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- adj = opp_ang_to_adj(opp,ang);
Description:
Given the length of the opposite side and the reference reference angle of a right triangle, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
adj = opp_ang_to_adj(8,45); // Returns: 8
Synopsis: Returns the adjacent side length from the reference reference angle and the length of the opposite side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_hyp()
Usage:
- adj = ang_opp_to_adj(ang,opp);
Description:
Given the reference reference angle of a right triangle, and the length of the side opposite of it, returns the length of the adjacent side.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
adj = ang_opp_to_adj(45,8); // Returns: 8
Synopsis: Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = hyp_adj_to_opp(hyp,adj);
Description:
Given the lengths of the hypotenuse and the adjacent side, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
opp = hyp_adj_to_opp(5,4); // Returns: 3
Synopsis: Returns the opposite side length from the lengths of the adjacent side and the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = adj_hyp_to_opp(adj,hyp);
Description:
Given the lengths of the adjacent side and the hypotenuse, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
opp = adj_hyp_to_opp(4,5); // Returns: 3
Synopsis: Returns the opposite side length from the length of the hypotenuse and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = hyp_ang_to_opp(hyp,ang);
Description:
Given the length of the hypotenuse of a right triangle and the reference reference angle, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
opp = hyp_ang_to_opp(8,30); // Returns: 4
Synopsis: Returns the opposite side length from the reference reference angle and the length of the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = ang_hyp_to_opp(ang,hyp);
Description:
Given the the reference reference angle and the length of the hypotenuse of a right triangle, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
opp = ang_hyp_to_opp(30,8); // Returns: 4
Synopsis: Returns the opposite side length from the length of the adjacent side and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = adj_ang_to_opp(adj,ang);
Description:
Given the length of the adjacent side of a right triangle, and the reference reference angle, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
opp = adj_ang_to_opp(8,45); // Returns: 8
Synopsis: Returns the opposite side length from the reference reference angle and the length of the adjacent side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- opp = ang_adj_to_opp(ang,adj);
Description:
Given the reference reference angle and the length of the adjacent side of a right triangle, returns the length of the opposite side.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
opp = ang_adj_to_opp(45,8); // Returns: 8
Synopsis: Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- hyp = adj_opp_to_hyp(adj,opp);
Description:
Given the length of the adjacent and opposite sides of a right triangle, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
hyp = adj_opp_to_hyp(3,4); // Returns: 5
Synopsis: Returns the hypotenuse length from the lengths of the opposite and adjacent sides.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- hyp = opp_adj_to_hyp(opp,adj);
Description:
Given the length of the opposite and adjacent sides of a right triangle, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
hyp = opp_adj_to_hyp(4,3); // Returns: 5
Synopsis: Returns the hypotenuse length from the length of the adjacent side and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- hyp = adj_ang_to_hyp(adj,ang);
Description:
For a right triangle, given the length of the adjacent side, and the reference reference angle, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
hyp = adj_ang_to_hyp(4,60); // Returns: 8
Synopsis: Returns the hypotenuse length from the reference reference angle and length of the adjacent side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- hyp = ang_adj_to_hyp(ang,adj);
Description:
For a right triangle, given the reference reference angle and length of the adjacent side, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
hyp = ang_adj_to_hyp(60,4); // Returns: 8
Synopsis: Returns the hypotenuse length from the length of the opposite side and the reference reference angle.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- hyp = opp_ang_to_hyp(opp,ang);
Description:
For a right triangle, given the length of the opposite side, and the reference reference angle, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
ang |
The reference reference angle of the right triangle in degrees |
Example 1:
include <BOSL2/std.scad>
hyp = opp_ang_to_hyp(4,30); // Returns: 8
Synopsis: Returns the hypotenuse length from the reference reference angle and the length of the opposite side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj()
Usage:
- hyp = ang_opp_to_hyp(ang,opp);
Description:
For a right triangle, given the reference reference angle and the length of the opposite side, returns the length of the hypotenuse.
Arguments:
| By Position | What it does |
|---|---|
ang |
The reference reference angle of the right triangle in degrees |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
hyp = opp_ang_to_hyp(30,4); // Returns: 8
Synopsis: Returns the reference reference angle from the lengths of the hypotenuse and the adjacent side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = hyp_adj_to_ang(hyp,adj);
Description:
For a right triangle, given the lengths of the hypotenuse and the adjacent side, returns the reference reference angle.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
ang = hyp_adj_to_ang(8,4); // Returns: 60 degrees
Synopsis: Returns the reference angle from the lengths of the adjacent side and the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = adj_hyp_to_ang(adj,hyp);
Description:
For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the reference reference angle.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
ang = adj_hyp_to_ang(4,8); // Returns: 60 degrees
Synopsis: Returns the reference reference angle from the lengths of the hypotenuse and the opposite side.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = hyp_opp_to_ang(hyp,opp);
Description:
For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the reference reference angle.
Arguments:
| By Position | What it does |
|---|---|
hyp |
The length of the hypotenuse of the right triangle. |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
ang = hyp_opp_to_ang(8,4); // Returns: 30 degrees
Synopsis: Returns the reference reference angle from the lengths of the opposite side and the hypotenuse.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = opp_hyp_to_ang(opp,hyp);
Description:
For a right triangle, given the lengths of the opposite side and the hypotenuse, returns the reference reference angle.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
hyp |
The length of the hypotenuse of the right triangle. |
Example 1:
include <BOSL2/std.scad>
ang = opp_hyp_to_ang(4,8); // Returns: 30 degrees
Synopsis: Returns the reference angle from the lengths of the adjacent and opposite sides.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = adj_opp_to_ang(adj,opp);
Description:
For a right triangle, given the lengths of the adjacent and opposite sides, returns the reference angle of the corner.
Arguments:
| By Position | What it does |
|---|---|
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
ang = adj_opp_to_ang(sqrt(3)/2,0.5); // Returns: 30 degrees
Synopsis: Returns the reference reference angle from the lengths of the opposite and adjacent sides.
Topics: Geometry, Trigonometry, Triangles
See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
Usage:
- ang = opp_adj_to_ang(opp,adj);
Description:
For a right triangle, given the lengths of the opposite and adjacent sides, returns the reference reference angle.
Arguments:
| By Position | What it does |
|---|---|
opp |
The length of the side of the right triangle that is opposite from the reference reference angle. |
adj |
The length of the side of the right triangle that is adjacent to the reference reference angle. |
Example 1:
include <BOSL2/std.scad>
ang = opp_adj_to_ang(0.5,sqrt(3)/2); // Returns: 30 degrees