How it works

Our Right Triangle Solver helps you quickly find the unknown sides and angles of any right-angled triangle. Just enter any two known values (sides or angles, excluding the 90° angle) and let the calculator do the rest. Ideal for geometry homework and trigonometry problems.

The Formula

In a right-angled triangle, with angle C = 90°: Pythagorean Theorem: a² + b² = c² Trigonometric Ratios (SOH CAH TOA):
sin(A) = a/c
cos(A) = b/c
tan(A) = a/b sin(B) = b/c
cos(B) = a/c
tan(B) = b/a Angle Sum: A + B = 90°

Worked Example

1. Example: Find Missing Values

   Imagine a right triangle where side 'a' (opposite Angle A) is 3 units and side 'b' (opposite Angle B) is 4 units. We want to find the hypotenuse 'c', Angle A, and Angle B. Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5. Using trigonometry: Angle A = arctan(a/b) = arctan(3/4) ≈ 36.87° Angle B = arctan(b/a) = arctan(4/3) ≈ 53.13° Check: 36.87° + 53.13° = 90°.

Tips, Assumptions & Limitations

• Ensure your input values are consistent (e.g., hypotenuse 'c' must be the longest side).
• Angles A and B must be acute (less than 90 degrees).
• You need at least two pieces of information (sides or angles) to solve the triangle.