Question

What are the exact values of a and b?

Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.

Answer 1

Angle A = 30° and AB is the hypotenuse (10), so the triangle is 30°–60°–90°. The side opposite 30° is half the hypotenuse and the side opposite 60° is (√3)/2 of the hypotenuse.

Thus
- a = BC = 10·sin30° = 10·(1/2) = 5
- b = CA = 10·cos30° = 10·(√3/2) = 5√3