The Right Triangle Solver turns two legs, a leg and the hypotenuse, or a side and an acute angle into every side, angle, area and perimeter via Pythagoras and SOHCAHTOA, drawn to scale.
Give any two pieces: two legs, a leg and the hypotenuse, or a side and an angle. The solver finds the missing sides, both acute angles, the area and the perimeter.
With two sides known, the Pythagorean theorem a² + b² = c² gives the third, where c is the hypotenuse opposite the right angle. With one side and an angle, the solver uses SOHCAHTOA: sin A = a/c, cos A = b/c and tan A = a/b.
The two acute angles always add up to 90°, so once angle A is known, angle B = 90° − A. From sides alone, the solver uses the inverse functions, such as A = arctan(a/b).
Because the two legs are perpendicular, the area is simply ½ × a × b. The perimeter is a + b + c. The diagram draws the triangle to scale with the right angle marked at C.