Right Triangle Calculator

Right Triangle - Solve mathematical problems with step-by-step solutions.

How the Right Triangle Calculator Works

A right triangle is a triangle with one 90-degree angle. It has unique properties that make calculations straightforward using the Pythagorean theorem and trigonometric functions. The side opposite the right angle is called the hypotenuse, and it's always the longest side.

Key Components

  • Pythagorean Theorem: a² + b² = c²
  • Triangle Parts: Hypotenuse (c), Leg a (base), Leg b (height), Two acute angles
  • Angle Sum: The two acute angles always add up to 90°

Key Formulas

Finding Sides

  • Hypotenuse: c = √(a² + b²)
  • Leg a: a = √(c² - b²)
  • Leg b: b = √(c² - a²)

Finding Angles

  • sin(θ) = opposite / hypotenuse
  • cos(θ) = adjacent / hypotenuse
  • tan(θ) = opposite / adjacent

Special Right Triangles

  • 45-45-90 Triangle: Sides ratio: 1 : 1 : √2
  • 30-60-90 Triangle: Sides ratio: 1 : √3 : 2

Real-World Applications

Construction & Architecture

Used to calculate roof slopes, stair dimensions, and ensure structures are square and level.

Navigation & Surveying

Calculate distances, heights, and angles for maps, GPS systems, and land measurements.

Frequently Asked Questions

How to use the Right Triangle Calculator

Follow these steps to get accurate results with the right triangle calculator.

  1. 1

    Enter your values

    Fill in the required input fields above. Units can be changed where available.

  2. 2

    Click Calculate

    Press the calculate button to compute results instantly in your browser.

  3. 3

    Review your results

    View the computed outputs and use related calculators for deeper analysis.