Question

In triangle ABC, angle A = 74°, a = 126, and b = 84. Find angle B.

A. 39.9°
B. 79.4°
C. 80.8°
D. impossible to tell

Answer 1

Currently doing the test and got A. 39.9°.

The full process is explained above. This is a confirmation that the other person is correct.

Answer 2

Triangle ABC
Angle A = 74°
a = 126
b = 84
Use the sine rule

`(a)/(sin A) = (b)/(sin B)`
Plug in the given

`(126)/(sin(74)) = (84)/(sin(B))`
Cross multiply
126 × sin(B) = 84 × sin(74)
Divide by 126

`(126sin(B))/(126) = (84sin(74))/(126)`
126 and 126 cancels out
sin(B) =
`(84sin(74))/(126)`
take sin inverse (
`sin^(-1)`)
B =
`sin^(-1)` (
`(84sin(74))/(126)`)
B = 39.85° = 39.9°