Question

What is the answer to this question?

Answer 1

Angle A of triangle ABC will be ...
  ∠A = θ₂ -θ₃ = 77° -26° = 51°
Angle B of triangle ABC will be ...
  ∠B = 180° -θ₂ -θ₁ = 180° -77° -44° = 59°
Then angle C will be ...
  ∠C = 180° -∠A -∠B = 180° -51° -59° = 70°

By the Law of Sines,
  a/sin(∠A) = c/sin(∠C)
  a = c×sin(∠A)/sin(∠C)
  a = (57 yd)×sin(51°)/sin(70°) ≈ 47.14 yd

The distance from B to C is 47.14 yd.