In order to find the measure of angle θ, use the law of sines for sides c and
a and angles A and C, just as follow:
a/sinA = c/sinθ
Solve for sinθ the previous equation:
a/sinA = c/sinθ
sinθ = (c sinA)/a
replace c = 30, a = 45 and A = 120°
sinθ = (30 sin120°)/45
sinθ = 0.577
Next, apply sin⁻¹ both sides to find the value of θ:
sin⁻¹(sin θ) = sin⁻¹ (0.577)
θ = sin⁻¹ (0.577)
θ = 35.26°
θ ≈ 35°
Hence, the value of θ is approximately 35°
