Question

Solve the triangle (picture provided)

Answer 1

Answer:

m∠A = 9.1°

m∠B = 10.9°

c = 54.2

The answer is (d)

Step-by-step explanation:

∵ a = 25

∵ b = 30

∵ m∠C = 160°

∴ c² = a² + b² - 2 × ab × cos(C)

∴ c² = 25² + 30² - 2(25)(30) × cos(160) = 2934.5389

∴ c = 54.2

∵ a/sin(A) = b/sin(B) = c/sin(C)

∵ 25/sin(A) = 54.2/sin(160)

∴ sin(A) = (25 × sin(160)) ÷ 54.2 = 0.1577584

∴ m∠A = 9.1°

∵ 30/sin(B) = 54.2/sin(160)

∴ sin(B) = (30 × sin(160)) ÷ 54.2 = 0.18931

∴ m∠B = 10.9°