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
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 |
Sine, cosine and tangent in one picture
For the angle A: sine is the opposite side divided by the hypotenuse, cosine is the adjacent side divided by the hypotenuse, and tangent is the opposite divided by the adjacent. All three ratios stay the same for a given angle no matter how large or small the triangle is, which is exactly why trigonometry tables and calculators work for any right triangle sharing that angle.