Question

In AABC, m/A = 74, a = 59.2, and c = 60.3. What are the two possible values for m/C, to

the nearest tenth?
1) 73.7 and 106.3
2) 73.7 and 163.7
3) 78.3 and 101.7
4)78.3 and 168.3

Answer 1

option 3

Explanation:

using the Sine Rule in Δ ABC

`(a)/(sinA)` =
`(c)/(sinC)` , that is

`(59.2)/(sin74)` =
`(60.3)/(sinC)` ( cross- multiply )

59.2 × sinC = 60.3 × sin74° ( divide both sides by 59.2 )

sinC =
`(60.3sin74)/(59.2)` , then

∠ C =
`sin^(-1)` (
`(60.3sin74)/(59.2)` ) ≈ 78.3° ( to the nearest tenth )

or ∠ C = 180° - 78.3° = 101.7°