Update index.html

Segment area calculator

Author: Gmac4247

index.html

@@ -3043,35 +3043,60 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
   <input id="parent-radius" type="number" value="0" step="any">
 
 <script>
-function segmentArea(length, height, angle, radius) {
-  // Sector area minus triangle area
-  return angle * radius ** 2 - (radius - height) * length / 2;
-}
+function segmentArea() {
+  // Read inputs
+  let h = parseFloat(document.getElementById('segment-height').value);
+  let r = parseFloat(document.getElementById('parent-radius').value);
+  let l = parseFloat(document.getElementById('chord-length').value);
+
+  // Detect which two are provided
+  let known = [!isNaN(h), !isNaN(r), !isNaN(l)].filter(Boolean).length;
+  if (known < 2) {
+    document.getElementById('segment-area').innerText =
+      'Error: Provide one more known property';
+    return;
+  }
 
-function calculateSegmentArea(height, radius = null, length = null) {
-  let angle, area;
-
-  if (radius) {
-    // Case 1: height + radius → derive chord length
-    const ratio = (radius - height) / radius;
-    angle = Acos(ratio);
-    length = 2 * radius * sin(angle / 2);
-  } else if (length) {
-    // Case 2: height + chord length → derive radius
-    radius = (height / 2) + (length ** 2) / (8 * height);
-    angle = 2 * Asin(length / (2 * radius));
-  } else {
+  // Case 1: height + radius known → derive length
+  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 =
-      'Error: Provide either radius or chord length.';
+      'Invalid input: must satisfy h ≤ r, l ≥ 2h, r ≥ h.';
     return;
   }
 
-  area = segmentArea(length, height, angle, radius);
+  // Compute angle and area
+  let angle = Acos((r - h) / r);
+  let area = angle * r ** 2 - (r - h) * (l / 2);
 
-  // Special semicircle cases
-  if (radius === height || height === length / 2) {
+  // Output with semicircle reminders
+  if (h === r) {
+    document.getElementById('segment-area').innerText =
+      `Semicircle area: ${area.toFixed(5)} square units`;
+  } else if (h === l / 2) {
+    document.getElementById('segment-area').innerText =
+      `Semicircle area: ${area.toFixed(5)} square units`;
+  } else if (l === 2 * r) {
     document.getElementById('segment-area').innerText =
-      `Area of semi-circle: ${area.toFixed(5)} square units`;
+      `Semicircle area: ${area.toFixed(5)} square units`;
   } else {
     document.getElementById('segment-area').innerText =
       `Area: ${area.toFixed(5)} square units`;