Right Triangle Calculator

Solve right triangles by finding missing sides, angles, area, and trigonometric functions with detailed step-by-step solutions.

Right Triangle Analysis

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Right Triangle Fundamentals

Definition

A right triangle has one angle that measures exactly 90 degrees (π/2 radians). The side opposite this right angle is called the hypotenuse and is the longest side.

Pythagorean Theorem

a² + b² = c²

Where a and b are the legs, and c is the hypotenuse. This fundamental relationship allows us to find any missing side when two sides are known.

Angle Relationships

  • One angle is always 90°
  • The other two angles are acute (less than 90°)
  • The sum of all angles is 180°
  • The two acute angles are complementary (sum to 90°)

Common Right Triangles

3-4-5: The most basic Pythagorean triple (3² + 4² = 5²)
5-12-13: Another common Pythagorean triple
45-45-90: Isosceles right triangle with legs in ratio 1:1:√2
30-60-90: Special triangle with sides in ratio 1:√3:2