Right triangle solver
Enter any two values (sides or angle) and solve the rest of a right triangle with trigonometry.
a, b are the legs, c is the hypotenuse. α is the angle at vertex A (opposite side a).
Enter any two values (at least one side) – the rest is computed.
How a right triangle is solved
A right triangle has one angle of 90°. The remaining two angles add up to 90° as well (because the angles of a triangle sum to 180°). To find the rest, it's enough to know two values, of which at least one is a side. Two tools are used:
Pythagorean theorem: c² = a² + b² • sin α = a/c • cos α = b/c • tan α = a/b
When you know two sides, find the third with the Pythagorean theorem, and the angles via inverse functions (arcsin, arccos, arctan). When you know a side and an angle, the remaining sides follow directly from the trigonometric functions. This is the most common practical use of trigonometry – from finding a tree's height to a roof's pitch to surveying in the field.
Note: the entered values must form a valid right triangle (e.g. the hypotenuse must be longer than each leg).