Solve a right triangle from its two legs — hypotenuse, angles, area, and perimeter. Enter the two legs.
Usage Tip
In a right triangle, the two non-right angles are complementary — they always add up to 90 degrees.
angle A = arctan(a ÷ b), area = (1 ÷ 2) a×b
The two acute angles always sum to 90 degrees.
Angle A is opposite leg a; angle B is its complement.
Area is half the product of the legs.
A right triangle has one 90 degree angle, and the two sides next to it are the legs. Given both legs, the hypotenuse comes from the Pythagorean theorem as the square root of the sum of the squared legs. The area is half the product of the legs, the perimeter adds all three sides, and each acute angle comes from an inverse tangent.
The two acute angles always add up to 90 degrees. Right triangles are used to find heights from distances, slopes of ramps and roofs, and the diagonal of a rectangle. Whole number examples such as 3, 4, 5 and 5, 12, 13 are useful for checking that a corner is square on a job site.