SOLVE RIGHT TRIANGLE GUIDE
How to find a missing right triangle angle
A right triangle contains a 90° angle and two acute angles. Those two acute angles add to 90°. If you already know one, subtract it from 90° to find the other.
B = 90° − A
If neither acute angle is known, use two side lengths and an inverse trigonometric function.
Choose a ratio that matches your known sides
Relative to angle A in our diagram, a is opposite, b is adjacent, and c is the hypotenuse.
| Known sides | Formula for A |
|---|---|
| Opposite and adjacent | A = arctan(a / b) |
| Opposite and hypotenuse | A = arcsin(a / c) |
| Adjacent and hypotenuse | A = arccos(b / c) |
Example: a = 3 m and b = 4 m
tan(A) = 3 / 4 = 0.75. Therefore A = arctan(0.75) ≈ 36.87°.
B = 90° − 36.87° ≈ 53.13°. The angles sum to 180° when the right angle is included.
Inverse does not mean reciprocal
arctan, sometimes written tan⁻¹ on a calculator, takes a tangent ratio and returns an angle. It is different from 1 / tan(angle). The same distinction applies to arcsin and arccos.
Check the angle unit
Degrees divide a full turn into 360 parts. Radians express the angle in terms of arc length on a unit circle; π radians equals 180°. A calculator in radian mode might return approximately 0.6435 for this example. That represents the same angle as 36.87°, not 0.6435°.
Solve Right Triangle displays the main angles in degrees and includes radian equivalents in the expandable ratio panel.
Solve the angle exampleFormula reference
For an independent explanation of these relationships, see Pearson’s right triangle formulas and worked examples.
Related right triangle guides
- How to find the hypotenuse
- SOH CAH TOA, explained visually
- 30–60–90 and 45–45–90 triangles
- Right triangles in practical measurements
- How to find a missing side of a right triangle
Open the right triangle calculator to check your own measurements.