Right Triangle Calculator
Enter any two values, with at least one side. Get every side and angle, plus area and perimeter.
How it works
With an angle and a side it uses SOH CAH TOA. With two sides it uses the Pythagorean theorem for the third and an inverse trig function for the angle. Side a is across from angle A, side b is next to it, and c is the hypotenuse.
Example
A right triangle has a 35° angle and a hypotenuse of 20. Find the other sides.
a = 11.4715, b = 16.383, c = 20
- Angle A
- 35°
- Angle B
- 55°
- Area
- 93.9693
- Perimeter
- 47.8546
Steps
- SOH: a = c · sin A = 20 · sin 35° = 11.4715.
- CAH: b = c · cos A = 20 · cos 35° = 16.383.
- The angles add to 180°, so B = 90° − 35° = 55°.
More examples
A right triangle has legs 7 and 24. Find the angles.
a = 7, b = 24, c = 25
- Angle A
- 16.2602°
- Angle B
- 73.7398°
- Area
- 84
- Perimeter
- 56
Steps
- Pythagorean theorem: c = √(a² + b²) = 25.
- A = tan⁻¹(a / b) = tan⁻¹(0.2917) = 16.2602°.
- The angles add to 180°, so B = 90° − 16.2602° = 73.7398°.
Angle A is 50° and the side next to it is 10. Find the other sides.
a = 11.9175, b = 10, c = 15.5572
- Angle A
- 50°
- Angle B
- 40°
- Area
- 59.5877
- Perimeter
- 37.4748
Steps
- TOA: a = b · tan A = 10 · tan 50° = 11.9175.
- CAH: c = b / cos A = 10 / cos 50° = 15.5572.
- The angles add to 180°, so B = 90° − 50° = 40°.
Common mistake
Set your calculator to degrees when checking by hand. In radian mode, sin 35 comes out negative.
Questions
How do I find an angle from two sides?
Use an inverse trig function. With opposite 3 and hypotenuse 5, A = sin⁻¹(3/5) ≈ 36.87°.
What do the two smaller angles add up to?
90°. Once you know one, the other is 90° minus it.
What if there is no right angle?
SOH CAH TOA only works on right triangles. Use the law of sines or the law of cosines instead.