Question

In a triangle ABC, if <B = 60° and the ratio of two sides is a: c= 2: square root 3+1, then <A=

Answer 1

Your answer is 75°.

To answer this question you need to use both the cosine rule and the sine rule. First, we need to find the length of side b by using the cosine rule, where a = 2 and c = √3 + 1. Then you substitute these into the equation:

b² = a² + c² - 2×a×c×cos(B)

b² = (2)² + (√3 + 1)² - 2×2×(√3 + 1)×cos(60)

b² = 4 + 4 + 2√3 - (4 - 4√3)×0.5

b² = 8 - 2 = 6

b = √6

Then you use this length in the sine rule, and find the angle:

$\frac{sin(A)}{\sqrt{3}+1 } =\frac{sin(60)}{\sqrt{6} }$

sin(A) = (√6 + √2)/4

A = 75

I hope this helps! Let me know if you have any questions