Question

Finding Missing Measurements
Consider the triangle.

Triangle A B C. Side A B has a length of 5, and side A C has a length of 5. Angle B is 30 degrees, angle C is 90 degrees, and angle A is unknown.

Angle A =
Angle B = 30°

Angle C = 90°

 

AB = 10

AC = 5

BC =

Answer 1

Angle A = 60°.

Because C = 90° and B = 30°, this is a 30°–60°–90° triangle. In that ratio the side opposite 30° is 1, opposite 60° is √3, and the hypotenuse is 2.

Here AC is opposite angle B (30°) and AC = 5, so the hypotenuse AB = 2·5 = 10 and the other leg BC = 5√3 ≈ 8.66.