Update index.html

Author: Gmac4247

index.html

@@ -1630,7 +1630,7 @@ <h3 style="margin:7px" itemprop="eduQuestionType">Area of a Triangle</h3>
 
     // Triangle validity check
   if (side1 + side2 <= side3 || side2 + side3 <= side1 || side3 + side1 <= side2) {
-    document.getElementById('triangle-area').innerText = 'The sum of the length of the two shorter sides of a triangle is larger than the third one.';
+    document.getElementById('triangle-area').innerText = 'The sum of the length of the two shorter sides of a triangle must be larger than the third one.';
     return;
   }
 
@@ -3034,6 +3034,16 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
 <meta itemprop="disambiguatingDescription" content="Area based on the A(circle)=3.2*radius^2 formula, instead of the pi=3.14... approximation">
 <meta itemprop="usageInfo" content="Enter the segment height and either the chord length or the radius of the parent circle. The other value will be discarded in the result.">
 
+<label for="segment-height">Segment Height:</label>
+<input id="segment-height" type="number" step="any" oninput="segmentArea()">
+<br>
+<label for="chord-length">Chord Length:</label>
+<input id="chord-length" type="number" step="any" oninput="segmentArea()">
+<br>
+<label for="parent-radius">Circle Radius:</label>
+<input id="parent-radius" type="number" step="any" oninput="segmentArea()">
+<br>
+<div id="segment-area"></div>
 <label for="segment-height">Segment Height:</label>
 <input id="segment-height" type="number" step="any" oninput="segmentArea()">
 <br>
@@ -3061,22 +3071,25 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
   if (!isNaN(h) && !isNaN(r) && isNaN(l)) {
     let angle = Acos((r - h) / r);
     l = 2 * r * sin(angle);
-    }
+    document.getElementById('chord-length').value = l.toFixed(5);
+  }
 
   // Case 2: height + length known → derive radius
   if (!isNaN(h) && !isNaN(l) && isNaN(r)) {
     r = (l ** 2 + 4 * h ** 2) / (8 * h);
-      }
+    document.getElementById('parent-radius').value = r.toFixed(5);
+  }
 
   // Case 3: length + radius known → derive height
   if (!isNaN(l) && !isNaN(r) && isNaN(h)) {
     h = r - Math.sqrt(r ** 2 - (l / 2) ** 2);
-      }
+    document.getElementById('segment-height').value = h.toFixed(5);
+  }
 
   // Validity checks
   if (h > r || l < 2 * h || r < h) {
     document.getElementById('segment-area').innerText =
-      'Invalid input: must satisfy h ≤ r, l ≥ 2h, r ≥ h.';
+      'The height of the segment must be shorter than the parent radius and half the length.';
     return;
   }
 
@@ -3099,7 +3112,7 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
       `Area: ${area.toFixed(5)} square units`;
   }
 }
-</script>
+	  </script>
   <p id="segment-area"></p>
 </div>
 </section>
@@ -3388,7 +3401,7 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Spherical Cap</h3>
 // Cap validity check
 
   if ( height > radius) {
-    document.getElementById('cap-volume').innerText = 'The height of a spherical cap is shorter than its radius.';
+    document.getElementById('cap-volume').innerText = 'The height of a spherical cap must be shorter than its radius.';
     return;
 }