Right Triangle Calculator

Published on: January 12, 2025

This Right Triangle Calculator helps you find a missing side in a right triangle using two known values. It can use two side lengths to find the hypotenuse with Pythagoras’ theorem, or use an angle and one side with a trigonometric ratio to find another side. Choose the mode that matches your problem, enter the given values, and the calculator will work out the missing side. It is a simple way to check answers, understand right triangle formulas, and practise basic trigonometry step by step.

Step-by-step method

  1. Identify what is given.
  2. Write the correct formula.
  3. Substitute the values and calculate.

Formulas:

Formula: hypotenuse from two sides

c = √(a² + b²)

Formula: opposite from angle and adjacent

opposite = adjacent × tan(θ)

Example 1: Side & Side: a = 3, b = 4

Step 1 - Identify what is given.

In this problem: The given sides are a = 3 and b = 4.

a=3b=4

Step 2 - Write the correct formula.

In this problem: Use the hypotenuse formula: c = √(a² + b²).

c=√(a² + b²)

Step 3 - Substitute the values and calculate.

In this problem: Substitute: c = √(3² + 4²) = 5.

c=√(3² + 4²)=5

Final answer: c = 5

Example 2: Angle & Side: θ = 30°, adjacent = 5

Step 1 - Identify what is given.

In this problem: The given values are θ = 30° and adjacent = 5.

θ=30°adjacent=5

Step 2 - Write the correct formula.

In this problem: Use the tangent relationship: opposite = adjacent × tan(θ).

opposite=adjacent×tan(θ)

Step 3 - Substitute the values and calculate.

In this problem: Substitute: opposite = 5 × tan(30°) = 2.88675135.

opposite=5×tan(30°)=2.88675135

Final answer: opposite = 2.88675135