Triangle Solver Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–white: #ffffff;
–dark-text: #333333;
–border-color: #dee2e6;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–dark-text);
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calc-container {
max-width: 900px;
margin: 30px auto;
background-color: var(–white);
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
padding: 30px;
border: 1px solid var(–border-color);
}
h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 20px;
}
.input-section, .output-section {
margin-bottom: 30px;
padding: 25px;
border: 1px solid var(–border-color);
border-radius: 6px;
background-color: #fdfdfd;
}
.input-group {
margin-bottom: 20px;
display: flex;
align-items: center;
gap: 15px;
flex-wrap: wrap;
}
.input-group label {
font-weight: 600;
flex-basis: 120px; /* Fixed width for labels */
text-align: right;
color: var(–dark-text);
}
.input-group input[type="number"] {
flex-grow: 1;
padding: 10px 12px;
border: 1px solid var(–border-color);
border-radius: 4px;
font-size: 1rem;
min-width: 150px; /* Minimum width for inputs */
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
.input-group input[type="number"]:focus {
border-color: var(–primary-blue);
outline: none;
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
}
.calc-button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: var(–primary-blue);
color: var(–white);
border: none;
border-radius: 5px;
font-size: 1.1rem;
font-weight: 600;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
text-transform: uppercase;
}
.calc-button:hover {
background-color: #003366;
transform: translateY(-2px);
}
.calc-button:active {
transform: translateY(0);
}
.output-section {
background-color: var(–success-green);
color: var(–white);
text-align: center;
}
#result h3 {
margin-top: 0;
color: var(–white);
font-size: 1.5rem;
}
#result p {
font-size: 1.2rem;
margin-bottom: 10px;
}
#result span {
font-weight: bold;
font-size: 1.8rem;
}
.error-message {
color: #dc3545;
font-weight: bold;
margin-top: 15px;
text-align: center;
}
.info-section {
margin-top: 30px;
padding: 25px;
border: 1px solid var(–border-color);
border-radius: 6px;
background-color: var(–white);
}
.info-section h2 {
color: var(–primary-blue);
text-align: left;
margin-bottom: 15px;
}
.info-section p, .info-section ul {
margin-bottom: 15px;
}
.info-section ul {
list-style: disc;
margin-left: 25px;
}
.info-section li {
margin-bottom: 8px;
}
/* Responsive adjustments */
@media (max-width: 768px) {
.input-group {
flex-direction: column;
align-items: stretch;
}
.input-group label {
text-align: left;
margin-bottom: 5px;
flex-basis: auto;
}
.input-group input[type="number"] {
width: 100%;
}
.calc-container {
padding: 20px;
}
}
Triangle Solver Calculator
Enter known sides and angles to solve for unknown values. Angles should be in degrees.
Solved Triangle
Results:
Side a:
Side b:
Side c:
Angle A:
Angle B:
Angle C:
Understanding Triangle Solving
Solving a triangle means finding all unknown sides and angles when some information is given. The fundamental rules governing triangles are:
- The sum of the interior angles of any triangle is always 180 degrees.
- The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Depending on the given information, different trigonometric laws are used:
- Law of Sines: Relates the lengths of the sides of a triangle to the sines of its opposite angles. It's stated as:
a/sin(A) = b/sin(B) = c/sin(C)
This law is useful when you have Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), or Side-Side-Angle (SSA – ambiguous case) information.
- Law of Cosines: Relates the lengths of the sides of a triangle to the cosine of one of its angles. It's stated as:
c² = a² + b² - 2ab * cos(C) (and permutations for other sides/angles)
This law is useful when you have Side-Side-Side (SSS) or Side-Angle-Side (SAS) information.
Common Triangle Solving Scenarios:
- Angle-Angle-Side (AAS): Given two angles and one non-included side. Calculate the third angle (180 – A – B). Then use the Law of Sines to find the other two sides.
- Angle-Side-Angle (ASA): Given two angles and the included side. Calculate the third angle (180 – A – B). Then use the Law of Sines to find the other two sides.
- Side-Side-Side (SSS): Given all three sides. Use the Law of Cosines to find one angle. Then use the Law of Sines or Cosines to find the other two angles. Be sure to check the Triangle Inequality Theorem first.
- Side-Angle-Side (SAS): Given two sides and the included angle. Use the Law of Cosines to find the third side. Then use the Law of Sines or Cosines to find the other two angles.
- Side-Side-Angle (SSA): This is the ambiguous case, as there might be zero, one, or two possible triangles. Use the Law of Sines to find an angle. If a valid solution is found, you may need to check for a second possible triangle by adjusting the found angle.
Use Cases:
Triangle solving has numerous applications in various fields:
- Navigation: Determining distances and positions using triangulation.
- Surveying: Measuring land areas and distances between points.
- Engineering and Architecture: Designing structures, calculating forces, and ensuring stability.
- Astronomy: Calculating distances to stars and planets.
- Computer Graphics and Game Development: Rendering 3D environments and calculating object interactions.
This calculator aims to simplify these calculations by applying the relevant trigonometric laws based on the inputs provided.
function solveTriangle() {
var sideA = parseFloat(document.getElementById('sideA').value);
var sideB = parseFloat(document.getElementById('sideB').value);
var sideC = parseFloat(document.getElementById('sideC').value);
var angleA = parseFloat(document.getElementById('angleA').value);
var angleB = parseFloat(document.getElementById('angleB').value);
var angleC = parseFloat(document.getElementById('angleC').value);
var resultSideA = document.getElementById('resultSideA');
var resultSideB = document.getElementById('resultSideB');
var resultSideC = document.getElementById('resultSideC');
var resultAngleA = document.getElementById('resultAngleA');
var resultAngleB = document.getElementById('resultAngleB');
var resultAngleC = document.getElementById('resultAngleC');
var outputSection = document.getElementById('outputSection');
var errorMessageDiv = document.getElementById('errorMessage');
errorMessageDiv.textContent = "; // Clear previous errors
outputSection.style.display = 'none'; // Hide previous results
var inputs = [sideA, sideB, sideC, angleA, angleB, angleC];
var validInputs = inputs.filter(function(input) { return !isNaN(input) && input !== null; });
// Helper function to check if a number is a valid angle (0 < angle 0 && angle 0)
function isValidSide(side) {
return typeof side === 'number' && side > 0;
}
// — Input Validation —
var knownValues = [];
if (isValidSide(sideA)) knownValues.push('sideA');
if (isValidSide(sideB)) knownValues.push('sideB');
if (isValidSide(sideC)) knownValues.push('sideC');
if (isValidAngle(angleA)) knownValues.push('angleA');
if (isValidAngle(angleB)) knownValues.push('angleB');
if (isValidAngle(angleC)) knownValues.push('angleC');
if (knownValues.length 180) {
errorMessageDiv.textContent = 'Error: The sum of the given angles exceeds 180 degrees.';
return;
}
if (angleSum === 180 && knownValues.length > 3 && (sideA || sideB || sideC)) {
// If all angles are given and sum to 180, and we are also given sides,
// there might be an inconsistency if not all sides are calculable perfectly.
// We proceed but this check can be more nuanced.
}
// — Store initial inputs to avoid overwriting —
var initialSideA = sideA;
var initialSideB = sideB;
var initialSideC = sideC;
var initialAngleA = angleA;
var initialAngleB = angleB;
var initialAngleC = angleC;
// — Calculation Logic —
var solved = false;
// Case 1: ASA (Angle-Side-Angle)
if (isValidAngle(angleA) && isValidAngle(angleB) && isValidSide(sideC)) {
angleC = 180 – angleA – angleB;
if (angleC > 0) {
var sinC = Math.sin(angleC * Math.PI / 180);
var k = sideC / sinC;
sideA = k * Math.sin(angleA * Math.PI / 180);
sideB = k * Math.sin(angleB * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles A and B do not form a valid triangle with side C.';
return;
}
} else if (isValidAngle(angleA) && isValidAngle(angleC) && isValidSide(sideB)) {
angleB = 180 – angleA – angleC;
if (angleB > 0) {
var sinB = Math.sin(angleB * Math.PI / 180);
var k = sideB / sinB;
sideA = k * Math.sin(angleA * Math.PI / 180);
sideC = k * Math.sin(angleC * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles A and C do not form a valid triangle with side B.';
return;
}
} else if (isValidAngle(angleB) && isValidAngle(angleC) && isValidSide(sideA)) {
angleA = 180 – angleB – angleC;
if (angleA > 0) {
var sinA = Math.sin(angleA * Math.PI / 180);
var k = sideA / sinA;
sideB = k * Math.sin(angleB * Math.PI / 180);
sideC = k * Math.sin(angleC * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles B and C do not form a valid triangle with side A.';
return;
}
}
// Case 2: AAS (Angle-Angle-Side) – similar to ASA after finding the third angle
if (!solved && isValidAngle(angleA) && isValidAngle(angleB) && isValidSide(sideA)) {
angleC = 180 – angleA – angleB;
if (angleC > 0) {
var sinA = Math.sin(angleA * Math.PI / 180);
var k = sideA / sinA;
sideB = k * Math.sin(angleB * Math.PI / 180);
sideC = k * Math.sin(angleC * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles A and B do not form a valid triangle with side A.';
return;
}
} else if (!solved && isValidAngle(angleA) && isValidAngle(angleC) && isValidSide(sideA)) {
angleB = 180 – angleA – angleC;
if (angleB > 0) {
var sinA = Math.sin(angleA * Math.PI / 180);
var k = sideA / sinA;
sideB = k * Math.sin(angleB * Math.PI / 180);
sideC = k * Math.sin(angleC * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles A and C do not form a valid triangle with side A.';
return;
}
} else if (!solved && isValidAngle(angleB) && isValidAngle(angleC) && isValidSide(sideB)) {
angleA = 180 – angleB – angleC;
if (angleA > 0) {
var sinB = Math.sin(angleB * Math.PI / 180);
var k = sideB / sinB;
sideA = k * Math.sin(angleA * Math.PI / 180);
sideC = k * Math.sin(angleC * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles B and C do not form a valid triangle with side B.';
return;
}
} else if (!solved && isValidAngle(angleA) && isValidAngle(angleC) && isValidSide(sideC)) {
angleB = 180 – angleA – angleC;
if (angleB > 0) {
var sinC = Math.sin(angleC * Math.PI / 180);
var k = sideC / sinC;
sideA = k * Math.sin(angleA * Math.PI / 180);
sideB = k * Math.sin(angleB * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Given angles A and C do not form a valid triangle with side C.';
return;
}
}
// Case 3: SAS (Side-Angle-Side)
if (!solved && isValidSide(sideA) && isValidSide(sideB) && isValidAngle(angleC)) {
// Law of Cosines for side c
sideC = Math.sqrt(sideA*sideA + sideB*sideB – 2*sideA*sideB*Math.cos(angleC * Math.PI / 180));
if (isValidSide(sideC)) {
// Law of Sines for angle A
var sinA = (sideA * Math.sin(angleC * Math.PI / 180)) / sideC;
angleA = Math.asin(sinA) * 180 / Math.PI;
// Calculate angle B (ensure it's not ambiguous)
angleB = 180 – angleC – angleA;
if (angleB > 0) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SAS input.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation resulted in an invalid side length.';
return;
}
} else if (!solved && isValidSide(sideA) && isValidSide(sideC) && isValidAngle(angleB)) {
sideB = Math.sqrt(sideA*sideA + sideC*sideC – 2*sideA*sideC*Math.cos(angleB * Math.PI / 180));
if (isValidSide(sideB)) {
var sinA = (sideA * Math.sin(angleB * Math.PI / 180)) / sideB;
angleA = Math.asin(sinA) * 180 / Math.PI;
angleC = 180 – angleB – angleA;
if (angleC > 0) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SAS input.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation resulted in an invalid side length.';
return;
}
} else if (!solved && isValidSide(sideB) && isValidSide(sideC) && isValidAngle(angleA)) {
sideA = Math.sqrt(sideB*sideB + sideC*sideC – 2*sideB*sideC*Math.cos(angleA * Math.PI / 180));
if (isValidSide(sideA)) {
var sinB = (sideB * Math.sin(angleA * Math.PI / 180)) / sideA;
angleB = Math.asin(sinB) * 180 / Math.PI;
angleC = 180 – angleA – angleB;
if (angleC > 0) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SAS input.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation resulted in an invalid side length.';
return;
}
}
// Case 4: SSS (Side-Side-Side)
if (!solved && isValidSide(sideA) && isValidSide(sideB) && isValidSide(sideC)) {
// Check Triangle Inequality Theorem
if (sideA + sideB > sideC && sideA + sideC > sideB && sideB + sideC > sideA) {
// Law of Cosines for angle C
var cosC = (sideA*sideA + sideB*sideB – sideC*sideC) / (2*sideA*sideB);
if (cosC >= -1 && cosC = -1 && cosB 0) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SSS input.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation for angle B resulted in an invalid cosine value.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation for angle C resulted in an invalid cosine value.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: The given side lengths do not satisfy the Triangle Inequality Theorem.';
return;
}
}
// Case 5: SSA (Side-Side-Angle) – Ambiguous Case (partial handling, assumes one solution or user inputs enough to make it non-ambiguous)
if (!solved && isValidSide(sideA) && isValidSide(sideB) && isValidAngle(angleA)) {
// Law of Sines to find angle B
var sinB = (sideB * Math.sin(angleA * Math.PI / 180)) / sideA;
if (sinB > 1 || sinB 0 && tempAngleC > 0) {
angleB = tempAngleB;
angleC = tempAngleC;
// Law of Sines for side c
sideC = (sideA * Math.sin(angleC * Math.PI / 180)) / Math.sin(angleA * Math.PI / 180);
solved = true;
} else {
// Try the second possible angle B if the first leads to an invalid triangle
tempAngleB = angleB_possible2;
tempAngleC = 180 – angleA – tempAngleB;
if (tempAngleB > 0 && tempAngleC > 0) {
angleB = tempAngleB;
angleC = tempAngleC;
sideC = (sideA * Math.sin(angleC * Math.PI / 180)) / Math.sin(angleA * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SSA input.';
return;
}
}
} else if (!solved && isValidSide(sideA) && isValidSide(sideC) && isValidAngle(angleA)) {
var sinC = (sideC * Math.sin(angleA * Math.PI / 180)) / sideA;
if (sinC > 1 || sinC 0 && tempAngleB > 0) {
angleC = tempAngleC;
angleB = tempAngleB;
sideB = (sideA * Math.sin(angleB * Math.PI / 180)) / Math.sin(angleA * Math.PI / 180);
solved = true;
} else {
tempAngleC = angleC_possible2;
tempAngleB = 180 – angleA – tempAngleC;
if (tempAngleC > 0 && tempAngleB > 0) {
angleC = tempAngleC;
angleB = tempAngleB;
sideB = (sideA * Math.sin(angleB * Math.PI / 180)) / Math.sin(angleA * Math.PI / 180);
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SSA input.';
return;
}
}
} else if (!solved && isValidSide(sideB) && isValidSide(sideC) && isValidAngle(angleA)) {
// Law of Sines for angle B
var sinB = (sideB * Math.sin(angleA * Math.PI / 180)) / sideA; // Need side A first
if (sinB > 1 || sinB 0 && tempAngleC > 0) {
angleB = tempAngleB;
angleC = tempAngleC;
// Now use Law of Cosines for side a, as we have SAS potentially
sideA = Math.sqrt(sideB*sideB + sideC*sideC – 2*sideB*sideC*Math.cos(angleA * Math.PI / 180));
if (isValidSide(sideA)) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation resulted in an invalid side length.';
return;
}
} else {
tempAngleB = angleB_possible2;
tempAngleC = 180 – angleA – tempAngleB;
if (tempAngleB > 0 && tempAngleC > 0) {
angleB = tempAngleB;
angleC = tempAngleC;
sideA = Math.sqrt(sideB*sideB + sideC*sideC – 2*sideB*sideC*Math.cos(angleA * Math.PI / 180));
if (isValidSide(sideA)) {
solved = true;
} else {
errorMessageDiv.textContent = 'Error: Law of Cosines calculation resulted in an invalid side length.';
return;
}
} else {
errorMessageDiv.textContent = 'Error: Calculated angles do not form a valid triangle for SSA input.';
return;
}
}
}
// — Final Checks and Display —
if (solved) {
// Re-calculate angles/sides if they were initially unknown and potentially rounded in intermediate steps
// Ensure all angles sum to 180 and sides satisfy triangle inequality if possible
// Re-calculate angles using Law of Cosines for more precision if possible, or verify sums
var finalAngleA = initialAngleA;
var finalAngleB = initialAngleB;
var finalAngleC = initialAngleC;
var finalSideA = initialSideA;
var finalSideB = initialSideB;
var finalSideC = initialSideC;
var calculatedAngles = [angleA, angleB, angleC].filter(isValidAngle);
var calculatedSides = [sideA, sideB, sideC].filter(isValidSide);
// Update fields with calculated values, respecting initial inputs
finalSideA = typeof initialSideA === 'number' && !isNaN(initialSideA) ? initialSideA : sideA;
finalSideB = typeof initialSideB === 'number' && !isNaN(initialSideB) ? initialSideB : sideB;
finalSideC = typeof initialSideC === 'number' && !isNaN(initialSideC) ? initialSideC : sideC;
finalAngleA = typeof initialAngleA === 'number' && !isNaN(initialAngleA) ? initialAngleA : angleA;
finalAngleB = typeof initialAngleB === 'number' && !isNaN(initialAngleB) ? initialAngleB : angleB;
finalAngleC = typeof initialAngleC === 'number' && !isNaN(initialAngleC) ? initialAngleC : angleC;
// Round results for cleaner display
var precision = 4; // Number of decimal places for results
resultSideA.textContent = finalSideA !== undefined ? finalSideA.toFixed(precision) : 'N/A';
resultSideB.textContent = finalSideB !== undefined ? finalSideB.toFixed(precision) : 'N/A';
resultSideC.textContent = finalSideC !== undefined ? finalSideC.toFixed(precision) : 'N/A';
resultAngleA.textContent = finalAngleA !== undefined ? finalAngleA.toFixed(precision) + '°' : 'N/A';
resultAngleB.textContent = finalAngleB !== undefined ? finalAngleB.toFixed(precision) + '°' : 'N/A';
resultAngleC.textContent = finalAngleC !== undefined ? finalAngleC.toFixed(precision) + '°' : 'N/A';
outputSection.style.display = 'block';
} else {
errorMessageDiv.textContent = 'Could not solve the triangle with the provided inputs. Please check the values and ensure at least two are given.';
}
}