Math

Right Triangle Side and Angle Calculator

Find the remaining sides and angle from one leg and its opposite angle.

Calculated Output

Other leg b 8.66

Hypotenuse c 10

Other angle B (°) 60

Formula: b = a/tan A, c = a/sin A, B = 90° − A

Step-by-Step Breakdown

1. Values used:

2. Leg a = 5

3. Angle opposite a = 30 °

5. Other leg b = 8.66

6. Hypotenuse c = 10

7. Other angle B = 60°

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The math behind it

Using trig: tan A = a/b so b = a/tan A; sin A = a/c so c = a/sin A. The other acute angle is 90° − A.

Leg 5 opposite 30° → b ≈ 8.66, c = 10, B = 60°.

Why must A be under 90°?

A right triangle's other two angles are acute, so each is less than 90°.