Question

Given the triangle below, what is m < b, rounded to the nearest tenth?

Answer 1

Option A:

m∠B = 42.1°

Solution:

Given data:

b = 18, c = 15 and m∠C = 34°

Using sine formula:

`$(b)/(\sin B)=(c)/(\sin C)`

Substitute the given values.

`$(18)/(\sin B)=(15)/(\sin 34^\circ)`

Do cross multiplication.

`${18} * {\sin 34^\circ}={15} *{\sin B}`

Divide by 15 on both sides.

`$\frac{{18} * {\sin 34^\circ}}{15} =\frac{{15} *{\sin B}}{15}`

`$\frac{{6} *0.559}{5} =\sin B`

`$0.6708=\sin B`

`$\sin ^(-1)0.6708= B`

`42.1^\circ =B`

Switch the sides.

m∠B = 42.1°

Option A is the correct answer.