Right Triangle Calculator
Solve any right triangle by entering two known sides or one side and an acute angle. This calculator finds all three sides, both acute angles, the area, and the perimeter using the Pythagorean theorem and trigonometric functions.
A right triangle has one 90-degree angle and two acute angles that sum to 90 degrees. The side opposite the right angle is the hypotenuse (always the longest side), and the other two sides are called legs.
Key Formulas:
- Pythagorean Theorem: a^2 + b^2 = c^2 (c is the hypotenuse)
- Trigonometric Ratios: sin(A) = opposite/hypotenuse = a/c, cos(A) = adjacent/hypotenuse = b/c, tan(A) = opposite/adjacent = a/b
- Area: A = 0.5 x leg1 x leg2
- Perimeter: P = a + b + c
Right triangles are the foundation of trigonometry and appear constantly in construction (roofs, ramps, stairs), navigation (distance and bearing calculations), physics (force decomposition), and computer graphics (rotation and projection). Common right triangles include the 3-4-5, 5-12-13, and 8-15-17 Pythagorean triples, as well as the 45-45-90 and 30-60-90 special triangles.