Find the side length of c

Question

Let a, b, c, A, B, C denote the side lengths and angles of a triangle, where A is the angle opposite side ◦◦

a,etc.Supposea=5,A=60 ,andB=75 .Find side length c.

Answer 1

When we have 2 angles and 1 side, we will use the sin law. If A = 60° and B = 75°, C = 180° - 60° - 75° = 45°

sin A/a = sin C/c substitute values.

sin (60°)/5 = sin (45°)/c

(√3/2)/5 = (√2/2)/c

√3/2 c = 5√2/2

c = 5√2/2 * 2/√3

c = 5√2/√3 = 5√2√3/3 = 5√6/3