Right Triangle Side and Angle Calculator
Solve any right triangle for missing sides and angles from any two known values.
Frequently Asked Questions
What information do I need to solve a right triangle?
You need any two known values among the three sides (legs a, b, and hypotenuse c) and the non-right angles (A and B), since the right angle (C = 90°) is always fixed. Two known values — whether two sides, a side and an angle, or (less commonly used here) two angles — fully determine the triangle, since trigonometric relationships and the Pythagorean theorem can derive everything else.
How do I solve for a missing angle if I know two sides?
Use inverse trigonometric functions. If you know the two legs (a, b): angle A = arctan(a/b). If you know a leg and the hypotenuse: angle A = arcsin(a/c) (using the leg opposite A) or angle A = arccos(b/c) (using the leg adjacent to A). Once you know one non-right angle, the other is simply 90° minus that angle, since all three angles of any triangle sum to 180°.
How do I find a missing side if I know one side and one angle?
Use the trigonometric ratios directly. If you know angle A and the hypotenuse c: a = c × sin(A) and b = c × cos(A). If you know angle A and leg a: b = a / tan(A) and c = a / sin(A). If you know angle A and leg b: a = b × tan(A) and c = b / cos(A). These come directly from the standard SOH-CAH-TOA relationships.
What naming convention does this calculator use for sides and angles?
The right angle is always at vertex C. Side a is opposite angle A, side b is opposite angle B, and c is the hypotenuse (opposite the right angle, and always the longest side). This is the standard convention used in most trigonometry textbooks, and angles A and B always sum to exactly 90° since C is fixed at 90° and all three angles total 180°.