Question

Use the triangle to answer the question. In the triangle, the length of side a is 5 ft., and m ∠ A = 60 ° . Find the exact lengths of sides b and c. Please show work.

Answer 1

• b = 5√3/3 or ≈ 2.9
• c = 10√3/3 or ≈ 5.8

Explanation:

This is a 30°-60°-90° triangle

• ∠A is 60°, so ∠B is 30°

Given also:

• a = 5 ft

As per property of 30°-60°-90° triangle, the ratio of sides is:

• b : a : c = 1 : √3 : 2

Since a = 5, the missing sides are:

• b/a = 1/√3 ⇒ b = a/√3 = 5/√3 = 5√3/3 ≈ 2.9
• b/c = 1/2 ⇒ c = 2b = 10√3/3 ≈ 5.8