Find the area of Triangle ABC. Round your answer to the nearest hundredth., m∠C = 68°, b = 12.9, c = 15.2

a. 51.90 c. 77.15 b. 60.10 d. 84.99

The area of the triangle = 84.99 units² ⇒ answer (d)

Step-by-step explanation:

∵ m∠C = 68°, b = 12.9, c = 15.2

To find the area of Δ we must find m∠A or a

∵ By using sin Rule:

∵ c/sin∠C = b/sin∠B

∴ 15.2/sin68 = 12.9/sinB

∴ sinB = (12.9 * sin68) : 15.2 = 0.7868863

∴ m∠B = 51.90°

∴ m∠A = 180 - 68 - 51.90 = 60.10°

∵ Area of Δ = 1/2 * S1 * S2 * sin including angle

∴ A = 1/2 * b * c * sinA

∴ A = 1/2 * 12.9 * 15.2 * sin60.10 = 84.99 units² ⇒ answer (d)