Find the indicated angle 𝜃. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 16, c = 12, and ∠C = 45°. Assume that 𝜃 is greater than 90°.)

Question

Round your answer to one decimal place.

Answer 1

sinθ/a = sinC/c

sinθ = a sinC/c = 16(√2/2)/12 = (2/3)√2

θ = sin^-1((2/3)√2 = 70.5°

180 - θ = 109.5°