How this calculator works
The missing side comes from the Pythagorean theorem. The acute angles then follow from the side ratios: angle A opposite leg a has sine a/c, and angle B is its complement, so A and B always add to exactly 90°. Together with the right angle the three angles sum to 180°.
Formula
c = √(a² + b²) or b = √(c² - a²); A = arcsin(a/c) and B = 90° - A.
Worked example
Legs of 3 and 4 give c = 5, A = arcsin(3/5) ≈ 36.8699° and B ≈ 53.1301°. Entering leg 3 with hypotenuse 5 gives the same triangle, with b = 4.
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Frequently asked questions
Why do the two acute angles add to 90°?
The right angle takes 90° of the 180° available in any triangle, so the two remaining angles must share the other 90° between them.
Which side is the hypotenuse?
Always the longest side, opposite the right angle. If your known leg equals or exceeds it, no right triangle exists.
Is the value I type in the field being solved used?
No. In two-legs mode the hypotenuse is calculated and your hypotenuse entry is ignored; in the leg and hypotenuse mode the other leg is calculated and its entry is ignored.