Angle of Right Angled Triangle Calculator

by

Angle of Right Angled Triangle Calculator

Enter any two side lengths to calculate the angles, the missing side, the perimeter, and the area of the triangle.

Calculation Results

Angle α (Alpha) –
Angle β (Beta) –
Third Side –
Area –
Perimeter –

Understanding Right-Angled Triangle Trigonometry

A right-angled triangle is a triangle in which one angle is exactly 90 degrees. This specific geometric shape allows us to use trigonometry to determine unknown sides and angles with precision using formulas like the Pythagorean Theorem and SOH CAH TOA.

The Primary Trigonometric Ratios

To calculate the angles of a right-angled triangle, we use the relationships between the sides:

  • Sine (sin): Opposite / Hypotenuse
  • Cosine (cos): Adjacent / Hypotenuse
  • Tangent (tan): Opposite / Adjacent

How to Use This Calculator

You only need two values to solve the entire triangle. Here are common scenarios:

  1. Given Two Legs (A and B): The calculator uses atan(A/B) to find the angles and the Pythagorean theorem (a² + b² = c²) to find the hypotenuse.
  2. Given a Leg and Hypotenuse: If you enter Side A and Side C, the calculator finds Angle α using asin(A/C) and calculates Side B using sqrt(C² - A²).

Real-World Example

Suppose you have a ladder leaning against a wall. The ladder is 10 feet long (Hypotenuse/Side C), and the base is 6 feet from the wall (Adjacent/Side B).

Calculation:

  • Angle β = arccos(6/10) = 53.13°
  • Height on wall (Side A) = sqrt(10² – 6²) = 8 feet
  • The angle between the ladder and the wall (Angle α) = 90° – 53.13° = 36.87°
function calculateTriangle() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var c = parseFloat(document.getElementById('sideC').value); var resAlpha = document.getElementById('resAlpha'); var resBeta = document.getElementById('resBeta'); var resSide = document.getElementById('resSide'); var resArea = document.getElementById('resArea'); var resPerim = document.getElementById('resPerim'); var resultArea = document.getElementById('resultArea'); var errorArea = document.getElementById('errorArea'); resultArea.style.display = 'none'; errorArea.style.display = 'none'; var inputs = 0; if (!isNaN(a) && a > 0) inputs++; if (!isNaN(b) && b > 0) inputs++; if (!isNaN(c) && c > 0) inputs++; if (inputs = c) { errorArea.innerHTML = "Hypotenuse (Side C) must be longer than the legs (Side A)."; errorArea.style.display = 'block'; return; } b = Math.sqrt(Math.pow(c, 2) – Math.pow(a, 2)); alpha = Math.asin(a / c) * (180 / Math.PI); beta = 90 – alpha; resSide.innerHTML = "Side B: " + b.toFixed(3); } else if (!isNaN(b) && !isNaN(c)) { // Given B and C if (b >= c) { errorArea.innerHTML = "Hypotenuse (Side C) must be longer than the legs (Side B)."; errorArea.style.display = 'block'; return; } a = Math.sqrt(Math.pow(c, 2) – Math.pow(b, 2)); alpha = Math.acos(b / c) * (180 / Math.PI); beta = 90 – alpha; resSide.innerHTML = "Side A: " + a.toFixed(3); } area = (a * b) / 2; perim = a + b + c; resAlpha.innerHTML = alpha.toFixed(2) + "°"; resBeta.innerHTML = beta.toFixed(2) + "°"; resArea.innerHTML = area.toFixed(2); resPerim.innerHTML = perim.toFixed(2); resultArea.style.display = 'block'; }

Leave a Comment