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How to find the angles in a right triangle

One angle is already known: C is 90°. The other two are acute, and they add up to 90°. Once you know A, B is 90° minus A. All three angles add up to 180°.

Match each angle to a side

Side a is opposite angle A. Side b is opposite angle B. Side c is opposite the right angle. The shorter leg is opposite the smaller acute angle. In a 3-4-5 triangle, side a = 3 is opposite the smaller angle, about 36.87°, and side b = 4 is opposite about 53.13°.

From the sides

1. Solve the missing side first if you only know two lengths. Hypotenuse and missing leg are the two side cases.
2. Angle A comes from the two legs: it is the angle whose opposite side is a and whose adjacent side is b.
3. Set B = 90° − A.
4. Keep C = 90°.

Sine, cosine, and tangent follow from the same sides. For angle A, sin A = a/c, cos A = b/c, and tan A = a/b. For angle B, the opposite and adjacent sides swap: sin B = b/c, cos B = a/c, and tan B = b/a.

From one given angle

If you already know an acute angle, you do not need arctangent. The other acute angle is the complement. Solving from one side and one angle sets those two angles exactly so that 30° and 60° stay 30° and 60°.

Common mistakes

• Labeling the right angle as A. In this convention the right angle is C.
• Putting the larger acute angle opposite the shorter side.
• Reporting only one acute angle and forgetting they must sum to 90°.

How the app does it

After a successful solve, the measurements list angle A, angle B, and angle C = 90°. Trigonometric values are grouped under Angle A and Angle B, each with sine, cosine, and tangent. The diagram uses the same labels: the right angle is at C, the horizontal side is a, and the vertical side is b.

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