Solving a right triangle
A right triangle has one angle of exactly 90 degrees. Because of that, knowing just two values, with at least one side, is enough to find everything else: both legs, the hypotenuse, both acute angles, the area, the perimeter, the altitude to the hypotenuse and the inscribed and circumscribed radii.
Enter any two of side a, side b, hypotenuse c, angle A and angle B. Side a is opposite angle A, side b is opposite angle B, and the right angle sits opposite the hypotenuse.
How it is calculated
c² = a² + b²
sin A = a ÷ c, cos A = b ÷ c, tan A = a ÷ b
B = 90° − A
Worked example
Side a = 5 and angle A = 30°
- Hypotenuse c
- 10
- Side b
- 8.66
- Angle B
- 60°
- Area
- 21.65
Two special triangles
| Triangle | Side ratio |
|---|---|
| 45° – 45° – 90° | 1 : 1 : √2 |
| 30° – 60° – 90° | 1 : √3 : 2 |