Question

Suppose an isosceles triangle ABC has A= pi/6 and b=5=c. What is the length of a^2.

5^2(2- sqrt 3)
5^2(sqrt3 -2)
5^2(2+ sqrt 3)
5^2 sqrt 3

Answer 1

check the picture below.

Answer 2

Option A. 5²(2-√3)

Explanation:

In an isosceles triangle b = c = 5 and ∠A = π/6

By cosine rule in any triangle

a² = b² + c² - 2bc cosA

By putting the values of b, c and ∠A in the equation

a² = 5² + 5² - 2×5×5×cos(π/6) = 25 + 25 - (50√3/2) = 50 - 25√3

a² = 25(2-√3) = 5²(2-√3)

Therefore the answer is Option A. 5²(2 - √3)