📐 Right Triangle Calculator

Fill in exactly two of the four fields below — leg a, leg b, hypotenuse c, or angle A (the angle opposite side a) — and the rest are solved automatically.

Leg a

Leg b

Hypotenuse c

Angle A (°, opposite side a)

Pythagoras for the sides, trigonometry for the angles

Two knowns fix a right triangle, because the right angle is already a third fact. The route taken depends on which pair you fill in:

c² = a² + b²                  area = a × b / 2
sin A = a / c    cos A = b / c    tan A = a / b
B = 90° − A

Press the 3-4-5 button and you get c = 5, angle A = 36.8699°, angle B = 53.1301°, an area of 6 and a perimeter of 12. Angle A came from tan⁻¹(3/4); everything else follows from it.

Which two values to give, and the traps

Exactly two fields, no more. Angle A is opposite leg a, so pairing it with b or c gives a different triangle than pairing it with a.
A leg cannot reach the hypotenuse. Entering a = 5 with c = 4 is refused rather than returning the square root of a negative number.
Angles are degrees, strictly between 0 and 90. At either end the triangle flattens to a line.
Everything is unitless. Feed it metres and the area comes back in square metres.

A practical use: a 6 m ladder set at 75° reaches 6 × sin 75° = 5.7956 m up the wall and stands 1.5529 m out from it. Enter c = 6 and angle A = 75 to see both.

Frequently asked questions

How do I find the hypotenuse of a right triangle?

Square both legs, add them, take the square root. Legs of 3 and 4 give 9 plus 16 = 25, so the hypotenuse is 5.

What are the angles in a 3-4-5 triangle?

36.87 and 53.13 degrees, plus the right angle. The smaller sits opposite the side of 3, and the two always add to 90.

How far up a wall does a 6 metre ladder reach at 75 degrees?

5.7956 metres, with the foot 1.5529 metres from the wall. Enter the ladder as the hypotenuse and 75 as angle A.