Right Triangle Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–border-color: #ddd;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calculator-container {
max-width: 800px;
margin: 30px auto;
background-color: #fff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
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: 20px;
border: 1px solid var(–border-color);
border-radius: 6px;
background-color: #fff;
}
.input-group {
display: flex;
flex-wrap: wrap;
gap: 20px;
margin-bottom: 20px;
align-items: center;
}
.input-group label {
flex: 0 0 150px;
font-weight: bold;
color: var(–primary-blue);
margin-right: 10px;
text-align: right;
}
.input-group input {
flex: 1 1 200px;
padding: 10px 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box;
}
.input-group input:focus {
outline: none;
border-color: var(–primary-blue);
box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.2);
}
.button-group {
text-align: center;
margin-top: 30px;
}
button {
background-color: var(–primary-blue);
color: white;
padding: 12px 25px;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
}
button:hover {
background-color: #003366;
}
#result {
text-align: center;
margin-top: 20px;
padding: 20px;
background-color: var(–success-green);
color: white;
font-size: 1.5em;
font-weight: bold;
border-radius: 6px;
}
.article-content {
margin-top: 40px;
background-color: #fff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid var(–border-color);
}
.article-content h2 {
text-align: left;
color: var(–primary-blue);
}
.article-content p, .article-content ul, .article-content ol {
margin-bottom: 15px;
}
.article-content ul {
list-style-type: disc;
padding-left: 20px;
}
.article-content li {
margin-bottom: 8px;
}
@media (max-width: 600px) {
.input-group {
flex-direction: column;
align-items: flex-start;
}
.input-group label {
text-align: left;
flex: none;
margin-bottom: 5px;
}
.input-group input {
width: 100%;
}
.calculator-container {
padding: 20px;
}
}
Right Triangle Calculator
Solve for unknown sides or angles of a right triangle.
Understanding Right Triangles and Their Calculations
A right triangle is a fundamental shape in geometry, defined by having one angle that measures exactly 90 degrees (a right angle). The sides adjacent to the right angle are called 'legs' (often denoted as 'a' and 'b'), and the side opposite the right angle is called the 'hypotenuse' (denoted as 'c').
Key Properties and Formulas:
- Pythagorean Theorem: This is the most famous property of right triangles. It states that the square of the hypotenuse ('c') is equal to the sum of the squares of the other two sides ('a' and 'b'). Mathematically:
a² + b² = c². This theorem is crucial for finding any missing side if two sides are known.
- Angle Sum Property: The sum of all angles in any triangle is 180 degrees. In a right triangle, since one angle is 90 degrees, the sum of the other two acute angles (let's call them Angle A and Angle B) must be 90 degrees:
Angle A + Angle B = 90°.
- Trigonometric Ratios (SOH CAH TOA): These ratios relate the angles of a right triangle to the lengths of its sides. They are essential for solving triangles when one side and one acute angle (or two sides) are known.
- Sine (sin):
sin(Angle) = Opposite / Hypotenuse
- Cosine (cos):
cos(Angle) = Adjacent / Hypotenuse
- Tangent (tan):
tan(Angle) = Opposite / Adjacent
How to Use This Calculator:
This calculator allows you to input known values for two sides and/or two angles of a right triangle. Based on your inputs, it will attempt to solve for the remaining unknown sides and angles using the principles described above.
- Inputting Sides: Enter the lengths of Side A (adjacent to Angle B, opposite Angle A) and Side B (adjacent to Angle A, opposite Angle B).
- Inputting Angles: Enter the measures of the acute angles (Angle A and Angle B) in degrees. Remember that both acute angles must sum to 90 degrees.
- Solving: The calculator needs at least two independent pieces of information (e.g., two sides, one side and one angle) to solve the triangle. If you provide redundant or contradictory information (e.g., all three sides, or two angles that don't sum to 90), the calculator might produce an error or unexpected results.
Use Cases:
Right triangle calculations are fundamental in numerous fields:
- Construction and Architecture: Determining roof slopes, ensuring corners are square, calculating diagonal supports.
- Navigation: Calculating distances and bearings, especially when dealing with perpendicular paths.
- Engineering: Analyzing forces, designing structures, solving problems in surveying.
- Physics: Calculating vectors, projectile motion, and forces acting at right angles.
- Mathematics Education: A core topic in trigonometry and geometry.
By accurately solving for unknown sides and angles, we can better understand spatial relationships and solve practical problems in design, measurement, and analysis.
function calculateRightTriangle() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var angleA_deg = parseFloat(document.getElementById("angleA").value);
var angleB_deg = parseFloat(document.getElementById("angleB").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "; // Clear previous results
var inputs = [sideA, sideB, angleA_deg, angleB_deg].filter(val => !isNaN(val));
var numKnown = inputs.length;
if (numKnown = calculatedHypotenuse) {
resultDiv.innerHTML = "Error: Side A cannot be greater than or equal to the hypotenuse.";
return;
}
calculatedSideB = Math.sqrt(calculatedHypotenuse * calculatedHypotenuse – sideA * sideA);
calculatedAngleB = Math.asin(calculatedSideB / calculatedHypotenuse) * (180 / Math.PI);
calculatedAngleA = 90 – calculatedAngleB;
}
// Case 2b: Side b and hypotenuse c known (if hypotenuse was input directly)
if (!isNaN(sideB) && !isNaN(calculatedHypotenuse) && isNaN(sideA)) {
if (sideB >= calculatedHypotenuse) {
resultDiv.innerHTML = "Error: Side B cannot be greater than or equal to the hypotenuse.";
return;
}
calculatedSideA = Math.sqrt(calculatedHypotenuse * calculatedHypotenuse – sideB * sideB);
calculatedAngleA = Math.asin(calculatedSideA / calculatedHypotenuse) * (180 / Math.PI);
calculatedAngleB = 90 – calculatedAngleA;
}
// Case 3: Side a and angle A known
if (!isNaN(sideA) && !isNaN(angleA_deg)) {
var angleA_rad = angleA_deg * (Math.PI / 180);
if (angleA_deg = 90) {
// Ignore if this angle is the only angle known besides right angle
} else {
if (isNaN(sideB)) sideB = sideA / Math.tan(angleA_rad);
if (isNaN(calculatedHypotenuse)) calculatedHypotenuse = sideA / Math.sin(angleA_rad);
if (isNaN(angleB_deg)) calculatedAngleB = 90 – angleA_deg;
}
}
// Case 4: Side b and angle A known
if (!isNaN(sideB) && !isNaN(angleA_deg)) {
var angleA_rad = angleA_deg * (Math.PI / 180);
if (angleA_deg = 90) {
// Ignore
} else {
if (isNaN(sideA)) sideA = sideB * Math.tan(angleA_rad);
if (isNaN(calculatedHypotenuse)) calculatedHypotenuse = sideB / Math.cos(angleA_rad);
if (isNaN(angleB_deg)) calculatedAngleB = 90 – angleA_deg;
}
}
// Case 5: Side a and angle B known
if (!isNaN(sideA) && !isNaN(angleB_deg)) {
var angleB_rad = angleB_deg * (Math.PI / 180);
if (angleB_deg = 90) {
// Ignore
} else {
if (isNaN(sideB)) sideB = sideA / Math.tan(angleB_rad);
if (isNaN(calculatedHypotenuse)) calculatedHypotenuse = sideA / Math.cos(angleB_rad);
if (isNaN(angleA_deg)) calculatedAngleA = 90 – angleB_deg;
}
}
// Case 6: Side b and angle B known
if (!isNaN(sideB) && !isNaN(angleB_deg)) {
var angleB_rad = angleB_deg * (Math.PI / 180);
if (angleB_deg = 90) {
// Ignore
} else {
if (isNaN(sideA)) sideA = sideB * Math.tan(angleB_rad);
if (isNaN(calculatedHypotenuse)) calculatedHypotenuse = sideB / Math.sin(angleB_rad);
if (isNaN(angleA_deg)) calculatedAngleA = 90 – angleB_deg;
}
}
// Case 7: Angle A and Angle B known
if (!isNaN(angleA_deg) && !isNaN(angleB_deg)) {
if (Math.abs((angleA_deg + angleB_deg) – 90) > 0.01) { // Allow for small floating point errors
resultDiv.innerHTML = "Error: Acute angles must sum to 90 degrees.";
return;
}
// Cannot solve sides with only angles unless one side is also provided
}
// — Consolidate and display results —
var results = [];
if (!isNaN(sideA)) results.push("Side A = " + sideA.toFixed(3));
if (!isNaN(sideB)) results.push("Side B = " + sideB.toFixed(3));
if (!isNaN(calculatedHypotenuse)) results.push("Hypotenuse (c) = " + calculatedHypotenuse.toFixed(3));
if (!isNaN(angleA_deg)) results.push("Angle A = " + angleA_deg.toFixed(3) + "°");
if (!isNaN(calculatedAngleA) && isNaN(angleA_deg)) results.push("Angle A = " + calculatedAngleA.toFixed(3) + "°");
if (!isNaN(angleB_deg)) results.push("Angle B = " + angleB_deg.toFixed(3) + "°");
if (!isNaN(calculatedAngleB) && isNaN(angleB_deg)) results.push("Angle B = " + calculatedAngleB.toFixed(3) + "°");
if (results.length === 0) {
resultDiv.innerHTML = "Could not solve with the provided inputs. Ensure you have at least two independent values.";
} else if (results.length < 5) { // Not all values solved
var missing = [];
if (isNaN(sideA)) missing.push("Side A");
if (isNaN(sideB)) missing.push("Side B");
if (isNaN(calculatedHypotenuse)) missing.push("Hypotenuse");
if (isNaN(angleA_deg) && isNaN(calculatedAngleA)) missing.push("Angle A");
if (isNaN(angleB_deg) && isNaN(calculatedAngleB)) missing.push("Angle B");
resultDiv.innerHTML = results.join("") + "Could not determine: " + missing.join(", ");
}
else {
resultDiv.innerHTML = results.join("");
}
}