Question

Use the Law of Sines to find the indicated angle 8. (Assume ZC = 64°. Round your answer to one decimal place.)

8 =
X°
56.3
C
80.2

B

Answer 1

θ ≈ 39.1°

Explanation:

Applying the law of sines in Δ ABC

`(a)/(sinA)` =
`(b)/(sinB)` =
`(c)/(sinC)`

where a, b, c are the sides opposite ∠ A , ∠ B, ∠ C

we are given

b = 56.3 , c = 80.2 , ∠ C = 64 , then using

`(b)/(sinB)` =
`(c)/(sinC)` ( substitute values )

`(56.3)/(sin0)` =
`(80.2)/(sin64)` ( cross- multiply )

80.2 × sinθ = 56.3 × sin64° ( divide both sides by 80.2 )

sinθ =
`(56.3sin64)/(80.2)` , then

θ =
`sin^(-1)` (
`(56.3sin64)/(80.2)` ) ≈ 39.1° ( to 1 decimal place )