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Right Triangle Calculator

Solve right triangles for angles and side lengths.

Math
Right Triangle Calculator
Solve right triangles for angles and side lengths.

Enter two sides to calculate the third.

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Your Go-To Tool for Right Triangles

This calculator is specifically designed for right-angled triangles. By entering any two known values (two sides, or a side and an angle), it uses the Pythagorean theorem and basic trigonometric functions (SOHCAHTOA) to quickly solve for all missing sides and angles.

The Formulas Explained

  • Pythagorean Theorem: a² + b² = c²
    • Where a and b are the legs and c is the hypotenuse.
  • Trigonometric Ratios (SOHCAHTOA):
    • sin(θ) = Opposite / Hypotenuse
    • cos(θ) = Adjacent / Hypotenuse
    • tan(θ) = Opposite / Adjacent

How to Use the Calculator

  1. Enter Known Values: Input any two values you know. For example, Side a and Side b.
  2. Leave the fields for the unknown values blank.
  3. Calculate: Click the button, and the calculator will solve for all the missing fields.

Real-World Example

You have a right triangle with one leg (a) of length 5 and the hypotenuse (c) of length 13.

  • Find Side b (Pythagorean Theorem): b = √(c² - a²) = √(169 - 25) = √144 = 12.
  • Find Angle A (SOH): sin(A) = Opposite/Hypotenuse = 5/13. A = arcsin(5/13) ≈ 22.6°.
  • Find Angle B: Since it's a right triangle, A + B = 90°. So B = 90° - 22.6° = 67.4°.

Frequently Asked Questions (FAQ)

  • What's the difference between this and the main Triangle Calculator? This one is specialized for right triangles only, making it simpler to use for those specific problems. The main Triangle Calculator can solve any type of triangle.
  • Do I need to enter the 90-degree angle? No, the calculator assumes one angle is 90 degrees.
  • What does 'adjacent' and 'opposite' mean? These terms are relative to an angle. The 'opposite' side is the one across from the angle. The 'adjacent' side is the leg next to the angle (that isn't the hypotenuse).