To calculate for the value of ∠ A, let us first find for the length of side B using the cosine law:
b^2 = a^2 + c^2 – 2 a c cos B
b^2 = 2^2 + (√3 + 1)^2 – 2 (2) (√3 + 1) cos 60
b^2 = 6
b = 2.45
Given two sides and the angle in between, we can calculate for ∠A using the sine law:
b / sin B = a / sin A
2.45 / sin 60 = 2 / sin A
sin A = 0.707
A = 45˚
Therefore the answer is letter A: 45
