.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
max-width: 600px;
margin: 20px auto;
border: 1px solid #ddd;
}
.calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.calculator-container p {
color: #555;
line-height: 1.6;
}
.calculator-inputs {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
color: #333;
font-weight: bold;
}
.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
width: 100%;
box-sizing: border-box;
}
.calculator-container button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
margin-right: 10px;
}
.calculator-container button:hover {
background-color: #0056b3;
}
.calculator-container button:last-of-type {
background-color: #6c757d;
}
.calculator-container button:last-of-type:hover {
background-color: #5a6268;
}
.calculator-results {
background-color: #e9ecef;
padding: 15px;
border-radius: 8px;
margin-top: 25px;
border: 1px solid #dee2e6;
}
.calculator-results h3 {
color: #333;
margin-top: 0;
border-bottom: 1px solid #ccc;
padding-bottom: 10px;
margin-bottom: 15px;
}
.calculator-results p {
margin-bottom: 8px;
color: #333;
}
.calculator-results span {
font-weight: bold;
color: #0056b3;
}
.article-content {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 600px;
margin: 40px auto;
padding: 0 20px;
color: #333;
line-height: 1.7;
}
.article-content h2, .article-content h3, .article-content h4 {
color: #333;
margin-top: 25px;
margin-bottom: 15px;
}
.article-content ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 15px;
}
.article-content li {
margin-bottom: 8px;
}
.article-content code {
background-color: #e0e0e0;
padding: 2px 4px;
border-radius: 3px;
font-family: 'Courier New', Courier, monospace;
}
function toRadians(degrees) {
return degrees * (Math.PI / 180);
}
function toDegrees(radians) {
return radians * (180 / Math.PI);
}
function clearTriangleInputs() {
document.getElementById('sideA').value = ";
document.getElementById('sideB').value = ";
document.getElementById('sideC').value = ";
document.getElementById('angleA').value = ";
document.getElementById('angleB').value = ";
document.getElementById('angleC').value = ";
document.getElementById('errorMessage').innerHTML = ";
document.getElementById('resultSideA').innerHTML = ";
document.getElementById('resultSideB').innerHTML = ";
document.getElementById('resultSideC').innerHTML = ";
document.getElementById('resultAngleA').innerHTML = ";
document.getElementById('resultAngleB').innerHTML = ";
document.getElementById('resultAngleC').innerHTML = ";
document.getElementById('resultPerimeter').innerHTML = ";
document.getElementById('resultArea').innerHTML = ";
}
function calculateTriangleTrigonometry() {
var a = parseFloat(document.getElementById('sideA').value);
var b = parseFloat(document.getElementById('sideB').value);
var c = parseFloat(document.getElementById('sideC').value);
var A_deg = parseFloat(document.getElementById('angleA').value);
var B_deg = parseFloat(document.getElementById('angleB').value);
var C_deg = parseFloat(document.getElementById('angleC').value);
var A = isNaN(A_deg) ? NaN : toRadians(A_deg);
var B = isNaN(B_deg) ? NaN : toRadians(B_deg);
var C = isNaN(C_deg) ? NaN : toRadians(C_deg);
var knownCount = 0;
if (!isNaN(a)) knownCount++;
if (!isNaN(b)) knownCount++;
if (!isNaN(c)) knownCount++;
if (!isNaN(A)) knownCount++;
if (!isNaN(B)) knownCount++;
if (!isNaN(C)) knownCount++;
var sideCount = 0;
if (!isNaN(a)) sideCount++;
if (!isNaN(b)) sideCount++;
if (!isNaN(c)) sideCount++;
var errorMessage = document.getElementById('errorMessage');
errorMessage.innerHTML = ";
clearResults(); // Clear previous results before displaying new ones or errors
if (knownCount < 3 || sideCount < 1) {
errorMessage.innerHTML = 'Please enter at least three values, including at least one side.';
return;
}
// Validate angles
if ((!isNaN(A_deg) && (A_deg = 180)) ||
(!isNaN(B_deg) && (B_deg = 180)) ||
(!isNaN(C_deg) && (C_deg = 180))) {
errorMessage.innerHTML = 'Angles must be between 0 and 180 degrees.';
return;
}
// Validate sides
if ((!isNaN(a) && a <= 0) || (!isNaN(b) && b <= 0) || (!isNaN(c) && c <= 0)) {
errorMessage.innerHTML = 'Side lengths must be positive.';
return;
}
var maxIterations = 10; // To prevent infinite loops in case of unsolvable or ambiguous inputs
for (var i = 0; i 0.01) { // Allow for floating point inaccuracies
errorMessage.innerHTML = 'The sum of the three angles exceeds 180 degrees.';
return;
}
// 2. Law of Sines
var ratio = NaN;
if (!isNaN(a) && !isNaN(A) && A > 0) ratio = a / Math.sin(A);
else if (!isNaN(b) && !isNaN(B) && B > 0) ratio = b / Math.sin(B);
else if (!isNaN(c) && !isNaN(C) && C > 0) ratio = c / Math.sin(C);
if (!isNaN(ratio)) {
if (isNaN(a) && !isNaN(A) && A > 0) a = ratio * Math.sin(A);
if (isNaN(b) && !isNaN(B) && B > 0) b = ratio * Math.sin(B);
if (isNaN(c) && !isNaN(C) && C > 0) c = ratio * Math.sin(C);
// Law of Sines to find angles (SSA case, potential ambiguity)
if (isNaN(A) && !isNaN(a) && !isNaN(b) && !isNaN(B) && b > 0) {
var sinA_val = a * Math.sin(B) / b;
if (sinA_val > 1 || sinA_val 0) {
var sinB_val = b * Math.sin(A) / a;
if (sinB_val > 1 || sinB_val 0) {
var sinC_val = c * Math.sin(A) / a;
if (sinC_val > 1 || sinC_val 0 && c > 0) {
var cosA_val = (b * b + c * c – a * a) / (2 * b * c);
if (cosA_val > 1 || cosA_val 0 && c > 0) {
var cosB_val = (a * a + c * c – b * b) / (2 * a * c);
if (cosB_val > 1 || cosB_val 0 && b > 0) {
var cosC_val = (a * a + b * b – c * c) / (2 * a * b);
if (cosC_val > 1 || cosC_val c && a + c > b && b + c > a)) {
errorMessage.innerHTML = 'The given side lengths do not form a valid triangle (Triangle Inequality Theorem).';
return;
}
// Check angle sum again for final solution
var finalAngleSum = toDegrees(A) + toDegrees(B) + toDegrees(C);
if (Math.abs(finalAngleSum – 180) > 0.1) { // Allow for small floating point errors
errorMessage.innerHTML = 'Calculated angles do not sum to 180 degrees. This might indicate an ambiguous case (SSA) or invalid input.';
return;
}
// Calculate Perimeter
var perimeter = a + b + c;
// Calculate Area (using Heron's formula if all sides are known, or 0.5*a*b*sin(C) if SAS is known)
var area = NaN;
if (!isNaN(a) && !isNaN(b) && !isNaN(c)) {
var s = perimeter / 2;
// Heron's formula can sometimes result in negative under sqrt due to floating point errors for very thin triangles
var heronTerm = s * (s – a) * (s – b) * (s – c);
if (heronTerm < 0) heronTerm = 0; // Clamp to 0 to avoid NaN from sqrt of negative
area = Math.sqrt(heronTerm);
} else if (!isNaN(a) && !isNaN(b) && !isNaN(C)) {
area = 0.5 * a * b * Math.sin(C);
} else if (!isNaN(b) && !isNaN(c) && !isNaN(A)) {
area = 0.5 * b * c * Math.sin(A);
} else if (!isNaN(c) && !isNaN(a) && !isNaN(B)) {
area = 0.5 * c * a * Math.sin(B);
}
if (isNaN(area) || area <= 0) {
errorMessage.innerHTML = 'Could not calculate a valid area. Please check inputs.';
return;
}
// Display results
document.getElementById('resultSideA').innerHTML = a.toFixed(4);
document.getElementById('resultSideB').innerHTML = b.toFixed(4);
document.getElementById('resultSideC').innerHTML = c.toFixed(4);
document.getElementById('resultAngleA').innerHTML = toDegrees(A).toFixed(4) + '°';
document.getElementById('resultAngleB').innerHTML = toDegrees(B).toFixed(4) + '°';
document.getElementById('resultAngleC').innerHTML = toDegrees(C).toFixed(4) + '°';
document.getElementById('resultPerimeter').innerHTML = perimeter.toFixed(4);
document.getElementById('resultArea').innerHTML = area.toFixed(4);
}
function clearResults() {
document.getElementById('resultSideA').innerHTML = '';
document.getElementById('resultSideB').innerHTML = '';
document.getElementById('resultSideC').innerHTML = '';
document.getElementById('resultAngleA').innerHTML = '';
document.getElementById('resultAngleB').innerHTML = '';
document.getElementById('resultAngleC').innerHTML = '';
document.getElementById('resultPerimeter').innerHTML = '';
document.getElementById('resultArea').innerHTML = '';
}
Understanding Triangle Trigonometry
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It's a fundamental tool in various fields, including engineering, physics, architecture, and surveying. This calculator helps you solve for unknown sides, angles, perimeter, and area of any general triangle using key trigonometric principles.
Key Concepts in Triangle Trigonometry
For any triangle (not just right-angled ones), two fundamental laws govern the relationships between its sides and angles:
1. The Law of Sines
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. If a triangle has sides a, b, c and opposite angles A, B, C respectively, then:
a / sin(A) = b / sin(B) = c / sin(C)
This law is particularly useful when you know:
- Two angles and one side (AAS or ASA).
- Two sides and a non-included angle (SSA – though this can sometimes lead to ambiguous cases with two possible triangles).
2. The Law of Cosines
The Law of Cosines is a generalization of the Pythagorean theorem and relates the lengths of the sides of a triangle to the cosine of one of its angles. It states:
c² = a² + b² - 2ab cos(C)a² = b² + c² - 2bc cos(A)b² = a² + c² - 2ac cos(B)
This law is essential when you know:
- Two sides and the included angle (SAS).
- All three sides (SSS).
3. Angle Sum Property
The sum of the interior angles of any triangle is always 180 degrees (or π radians). So, A + B + C = 180°.
4. Perimeter and Area
- Perimeter: The sum of all three sides:
Perimeter = a + b + c.
- Area:
- If you know two sides and the included angle (SAS):
Area = 0.5 * a * b * sin(C) (or similar variations).
- If you know all three sides (SSS), you can use Heron's Formula:
First, calculate the semi-perimeter s = (a + b + c) / 2.
Then, Area = sqrt(s * (s - a) * (s - b) * (s - c)).
How to Use the Triangle Trigonometry Calculator
To use this calculator, simply input at least three known values of your triangle. You must include at least one side length. The calculator will then use the principles of trigonometry to determine the remaining unknown sides, angles, the perimeter, and the area of the triangle.
- Enter side lengths (a, b, c) in any unit (e.g., cm, meters, inches).
- Enter angles (A, B, C) in degrees.
- Click "Calculate Triangle" to see the results.
- Click "Clear" to reset all fields.
Examples
Example 1: Side-Side-Side (SSS)
Suppose you have a triangle with sides a = 5, b = 6, and c = 7.
Input:
- Side a: 5
- Side b: 6
- Side c: 7
Output (approximate):
- Angle A: 44.4153°
- Angle B: 57.1218°
- Angle C: 78.4629°
- Perimeter: 18.0000
- Area: 14.6969
Example 2: Side-Angle-Side (SAS)
Consider a triangle where side a = 10, angle C = 45°, and side b = 12.
Input:
- Side a: 10
- Side b: 12
- Angle C: 45
Output (approximate):
- Side c: 8.5846
- Angle A: 54.0000°
- Angle B: 81.0000°
- Perimeter: 30.5846
- Area: 42.4264
Example 3: Angle-Side-Angle (ASA)
Let's say you have a triangle with angle A = 30°, side c = 15, and angle B = 70°.
Input:
- Angle A: 30
- Side c: 15
- Angle B: 70
Output (approximate):
- Side a: 7.6604
- Side b: 14.3397
- Angle C: 80.0000°
- Perimeter: 37.0001
- Area: 53.6231
This calculator provides a powerful way to explore and understand the relationships within triangles, making complex trigonometric calculations accessible and straightforward.