Right Triangle Calculator
Solve all sides and angles of a right triangle from two known values.
About Right Triangle Calculations
A right triangle contains one 90° angle (the right angle) and two acute angles that sum to 90°. The side opposite the right angle is the hypotenuse (c), the longest side. The other two sides are called legs (a and b). Right triangles are fully determined once any two independent measurements are known.
Trigonometric functions connect the sides and angles: sin(A) = a/c, cos(A) = b/c, tan(A) = a/b. These relationships allow you to find any unknown from a known side and angle. The mnemonic SOH-CAH-TOA helps remember these: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Right triangles appear everywhere in architecture, engineering, and navigation. Any time you need to calculate a height, distance, or angle using indirect measurement, right triangle trigonometry provides the solution. From ramp slopes to roof pitches to satellite signal paths, this foundational geometry is indispensable.
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For a related calculation, use Triangle Calculator to solve any triangle from SSS, SAS, ASA, AAS, or SSA inputs using the Law of Sines and Law of Cosines. Alternatively, use Pythagorean Theorem Calculator to given any two sides of a right triangle, solve for the third using the Pythagorean theorem c²=a²+b².
For the underlying method, read How to Solve Any Triangle: Law of Sines vs. Law of Cosines.