Question

Geometry - Law of Sines question #17. Please help, I am stuck.

Answer 1

By the law of sines, m∠EFG is such that

sin(m∠EFG) / (8 in.) = sin(m∠G) / (7.5 in)

so you need to find m∠G.

The interior angles to any triangle sum to 180°, so

m∠DEG = m∠D + m∠G + 43°

m∠DEG + m∠D + m∠G = 2 (m∠D + m∠G) + 43°

180° = 2 (m∠D + m∠G) + 43°

137° = 2 (m∠D + m∠G)

68.5° = m∠D + m∠G

But ∆DEG is isosceles, so m∠D = m∠G, which means

68.5° = 2 m∠G

34.25° = m∠G

Then

sin(m∠EFG) = (8 in.) sin(34.25°) / (7.5 in)

m∠EFG ≈ sin⁻¹(0.600325) ≈ 36.8932°