If ΔABC, BC = 12.35, AC = 8.75 centimeters, and m∠B = 37°, what are m∠A and m∠C in two decimal places?
A. m∠A ≈ 25.24°, m∠C ≈ 117.76°
B. m∠A ≈ 58.15°, m∠C ≈ 84.85°
C. m∠A ≈ 25.24°, m∠C ≈ 64.76° D
. m∠A ≈ 58.15°, m∠C ≈ 31.85°
We apply the sine rule here: a/sin(A) = b/sin(B) = c/sin(C) The side opposite to angle B is AC The side opposite to angle A is BC The side opposite to angle C is AB 8.75/sin(37) = 12.35/sin(A) A = 58.15° The sum of the three angles is 180° Angle C = 180 - 58.15 - 37 Angle C = 84.85° The answer is B
