Question

Solve the triangle. Round your answers to the nearest tenth.

Answer 1

m∠A ≈ 43°

m∠B ≈ 55°

mBC ≈ 20

Explanation:

Law of Sines:
`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

Step 1: Find m∠B

`(29)/(sin82) =(24)/(sinB)`

Step 2: Solve for ∠B

29sinB = 24sin82°

sinB = 24sin82°/29

B = sin⁻¹(24sin82°/29)

B = 55.038°

Step 3: Find m∠A

180 - (55.038 + 82)

180 - 137.038

m∠A = 42.962°

Step 4: Find BC

`(29)/(sin82) =(BC)/(sin42.962)`

Step 5: Solve for BC

29sin42.962° = BCsin82°

BC = 29sin42.962°/sin82°

BC = 19.9581