Find the area of Triangle ABC. Round your answer to the nearest tenth. m∠A = 52°, a = 9.71, c = 9.33

a. 44.5 c. 49.4 b. 33.6 d. 77.1

The area of the Δ = 44.5 units² ⇒ answer (a)

Step-by-step explanation:

∵ a = 9.71, c = 9.33, m∠A = 52°

To find the area of the triangle we must have:

m∠B or b

By using sin Rule:

∵ a/sin∠A = c/sin∠C

∴ 9.71/sin52 = 9.33/sinC

∴ sinC = (9.33 * sin52) : 9.71 = 0.757172

∴ m∠C = 49.2°

∴ m∠B = 180 - 52 - 49.2 = 78.8°

∵ A the Δ = 1/2 * a * c * sinB

∴ A = 1/2 * 9.71 * 9.33 * sin78.8 = 44.5 units² ⇒ answer (a)