function toRadians(degrees) {
return degrees * (Math.PI / 180);
}
function toDegrees(radians) {
return radians * (180 / Math.PI);
}
function round(value, decimals) {
if (isNaN(value)) return ";
return Number(Math.round(value + 'e' + decimals) + 'e-' + decimals);
}
function displayError(message) {
document.getElementById('errorMessage').innerHTML = " + message + ";
clearResults(); // Clear previous results when an error occurs
}
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('errorMessage').innerHTML = ";
}
function clearInputsAndResults() {
document.getElementById('sideA').value = ";
document.getElementById('sideB').value = ";
document.getElementById('sideC').value = ";
document.getElementById('angleA').value = ";
document.getElementById('angleB').value = ";
clearResults();
}
function calculateTriangle() {
clearResults(); // Clear previous results and errors
var a_input = parseFloat(document.getElementById('sideA').value);
var b_input = parseFloat(document.getElementById('sideB').value);
var c_input = parseFloat(document.getElementById('sideC').value);
var A_deg_input = parseFloat(document.getElementById('angleA').value);
var B_deg_input = parseFloat(document.getElementById('angleB').value);
var known = {
a: !isNaN(a_input) && a_input > 0 ? a_input : null,
b: !isNaN(b_input) && b_input > 0 ? b_input : null,
c: !isNaN(c_input) && c_input > 0 ? c_input : null,
A: !isNaN(A_deg_input) && A_deg_input > 0 && A_deg_input 0 && B_deg_input < 90 ? B_deg_input : null
};
var countKnown = 0;
for (var key in known) {
if (known[key] !== null) {
countKnown++;
}
}
if (countKnown = c) {
displayError("Side 'a' cannot be greater than or equal to hypotenuse 'c'.");
return;
}
b = Math.sqrt(c * c – a * a);
A_rad = Math.asin(a / c);
B_rad = Math.acos(a / c);
} else if (known.b !== null && known.c !== null) { // b and c
b = known.b;
c = known.c;
if (b >= c) {
displayError("Side 'b' cannot be greater than or equal to hypotenuse 'c'.");
return;
}
a = Math.sqrt(c * c – b * b);
B_rad = Math.asin(b / c);
A_rad = Math.acos(b / c);
}
// Case 2: One side and one angle
else if (known.a !== null && known.A !== null) { // a and A
A_deg = known.A;
A_rad = toRadians(A_deg);
B_deg = 90 – A_deg;
B_rad = toRadians(B_deg);
c = a_input / Math.sin(A_rad);
b = a_input / Math.tan(A_rad);
} else if (known.a !== null && known.B !== null) { // a and B
B_deg = known.B;
B_rad = toRadians(B_deg);
A_deg = 90 – B_deg;
A_rad = toRadians(A_deg);
c = a_input / Math.cos(B_rad);
b = a_input * Math.tan(B_rad);
} else if (known.b !== null && known.A !== null) { // b and A
A_deg = known.A;
A_rad = toRadians(A_deg);
B_deg = 90 – A_deg;
B_rad = toRadians(B_deg);
c = b_input / Math.cos(A_rad);
a = b_input * Math.tan(A_rad);
} else if (known.b !== null && known.B !== null) { // b and B
B_deg = known.B;
B_rad = toRadians(B_deg);
A_deg = 90 – B_deg;
A_rad = toRadians(A_deg);
c = b_input / Math.sin(B_rad);
a = b_input / Math.tan(B_rad);
} else if (known.c !== null && known.A !== null) { // c and A
A_deg = known.A;
A_rad = toRadians(A_deg);
B_deg = 90 – A_deg;
B_rad = toRadians(B_deg);
a = c_input * Math.sin(A_rad);
b = c_input * Math.cos(A_rad);
} else if (known.c !== null && known.B !== null) { // c and B
B_deg = known.B;
B_rad = toRadians(B_deg);
A_deg = 90 – B_deg;
A_rad = toRadians(A_deg);
a = c_input * Math.cos(B_rad);
b = c_input * Math.sin(B_rad);
}
// Case 3: Two angles (and implicitly 90 degrees) – requires a side
else if (known.A !== null && known.B !== null) {
A_deg = known.A;
B_deg = known.B;
if (Math.abs(A_deg + B_deg – 90) > 0.001) {
displayError("Angles A and B must sum to 90 degrees for a right triangle.");
return;
}
displayError("To solve, please provide at least one side along with the two angles.");
return;
} else {
displayError("Please provide a valid combination of inputs (e.g., two sides, or one side and one angle).");
return;
}
// Convert calculated angles back to degrees if they were derived from radians
if (A_deg === undefined || isNaN(A_deg)) A_deg = toDegrees(A_rad);
if (B_deg === undefined || isNaN(B_deg)) B_deg = toDegrees(B_rad);
// Final validation for calculated values (e.g., no negative lengths)
if (a <= 0 || b <= 0 || c <= 0 || A_deg <= 0 || B_deg = 90 || B_deg >= 90) {
displayError("Invalid triangle dimensions calculated. Please check your inputs.");
return;
}
// Round all results
a = round(a, 4);
b = round(b, 4);
c = round(c, 4);
A_deg = round(A_deg, 4);
B_deg = round(B_deg, 4);
// Display results
document.getElementById('resultSideA').innerHTML = a + ' units';
document.getElementById('resultSideB').innerHTML = b + ' units';
document.getElementById('resultSideC').innerHTML = c + ' units';
document.getElementById('resultAngleA').innerHTML = A_deg + ' °';
document.getElementById('resultAngleB').innerHTML = B_deg + ' °';
document.getElementById('resultAngleC').innerHTML = '90 °'; // Always 90 for right triangle
}
Understanding the Right Triangle Calculator
A right triangle is a special type of triangle that has one angle measuring exactly 90 degrees (a right angle). The sides of a right triangle have specific relationships that allow us to calculate unknown lengths and angles if we know at least two pieces of information (with at least one being a side).
Key Components of a Right Triangle
Legs (Sides 'a' and 'b'): These are the two sides that form the right angle. Side 'a' is typically opposite Angle A, and Side 'b' is opposite Angle B.
Hypotenuse (Side 'c'): This is the longest side of the right triangle and is always opposite the 90-degree angle.
Angles (A, B, C): Angle C is always 90 degrees. Angles A and B are the two acute angles (less than 90 degrees), and their sum always equals 90 degrees (A + B = 90°).
Fundamental Principles
1. The Pythagorean Theorem
This fundamental theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it's expressed as:
a² + b² = c²
This theorem is crucial when you know two sides and need to find the third.
2. Trigonometric Ratios (SOH CAH TOA)
Trigonometry provides relationships between the angles and the ratios of the sides of a right triangle. These are often remembered by the acronym SOH CAH TOA:
SOH: Sine = Opposite / Hypotenuse sin(A) = a / c sin(B) = b / c
CAH: Cosine = Adjacent / Hypotenuse cos(A) = b / c cos(B) = a / c
TOA: Tangent = Opposite / Adjacent tan(A) = a / b tan(B) = b / a
These ratios are used to find unknown sides when an angle and a side are known, or to find unknown angles when two sides are known (using inverse trigonometric functions like arcsin, arccos, arctan).
How to Use the Calculator
Our Right Triangle Calculator is designed to be intuitive:
Enter Known Values: Input any two values you know about the right triangle into the corresponding fields. You must provide at least one side length. For example, you can enter two side lengths (e.g., side 'a' and side 'b'), or one side length and one acute angle (e.g., side 'c' and angle 'A').
Click "Calculate Triangle": The calculator will then use the appropriate formulas (Pythagorean theorem and trigonometric ratios) to determine all the missing side lengths and angles.
View Results: The calculated values for all sides and angles will be displayed in the "Results" section. Side lengths will be in "units" (e.g., meters, feet, inches, etc., depending on what you input), and angles will be in degrees.
Clear All: Use the "Clear All" button to reset all input fields and results for a new calculation.
Examples
Example 1: Knowing Two Legs
Suppose you have a right triangle where:
Side 'a' = 3 units
Side 'b' = 4 units
Calculation Steps:
Find Hypotenuse 'c': Using the Pythagorean theorem:
c² = a² + b²c² = 3² + 4² = 9 + 16 = 25c = √25 = 5 units
Find Angle 'A': Using tangent:
tan(A) = a / b = 3 / 4 = 0.75A = arctan(0.75) ≈ 36.87°
Find Angle 'B': Since A + B = 90°:
B = 90° - A = 90° - 36.87° ≈ 53.13°
Calculator Input: Enter '3' for Side 'a' and '4' for Side 'b'. Calculator Output: Side 'c' = 5 units, Angle 'A' ≈ 36.87°, Angle 'B' ≈ 53.13°.
Example 2: Knowing One Leg and One Angle
Suppose you have a right triangle where:
Side 'a' = 6 units
Angle 'A' = 30°
Calculation Steps:
Find Angle 'B': Since A + B = 90°:
B = 90° - A = 90° - 30° = 60°
Find Hypotenuse 'c': Using sine:
sin(A) = a / cc = a / sin(A) = 6 / sin(30°) = 6 / 0.5 = 12 units
Find Side 'b': Using tangent:
tan(A) = a / bb = a / tan(A) = 6 / tan(30°) ≈ 6 / 0.5774 ≈ 10.3923 units
Calculator Input: Enter '6' for Side 'a' and '30' for Angle 'A'. Calculator Output: Side 'b' ≈ 10.3923 units, Side 'c' = 12 units, Angle 'B' = 60°.
This calculator is a handy tool for students, engineers, architects, and anyone needing to quickly solve for unknown dimensions in right-angled triangles.