How to Find an Angle in a Right Triangle

Every right triangle has one 90-degree angle. The other two angles are acute (less than 90°) and always add up to exactly 90°. To find these missing angles, you must use basic trigonometry.

If you don't want to deal with complex formulas, just plug your side lengths into our Right Angle Calculator Triangle for an instant, accurate answer.

Using Inverse Trigonometry (SOH CAH TOA)

To find an angle, you need to know the lengths of at least two sides. Depending on which sides you know relative to the angle you are trying to find, you will use one of three inverse trigonometric functions:

• ArcSine (sin^-1): Use this if you know the side Opposite the angle and the Hypotenuse.
• ArcCosine (cos^-1): Use this if you know the side Adjacent to the angle and the Hypotenuse.
• ArcTangent (tan^-1): Use this if you know the Opposite side and the Adjacent side.

Step-by-Step Example

Imagine a triangle where the side opposite to your unknown Angle A is 5, and the side adjacent to Angle A is 12. Because you know the Opposite and Adjacent sides, you will use ArcTangent.

1. Set up the ratio: Opposite / Adjacent = 5 / 12 ≈ 0.4167
2. Apply ArcTangent: tan^-1(0.4167)
3. Calculate: Angle A ≈ 22.6°

Once you find Angle A, finding the final angle (Angle B) is incredibly easy. Because the two acute angles must add up to 90°, simply subtract Angle A from 90°:

90° - 22.6° = 67.4°