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
Accepted Solution
A:
Answer: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 bBy 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)