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:

$\frac{b}{\sin B}=\frac{c}{\sin C}$

Substitute the given values.

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

Do cross multiplication.

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

Divide by 15 on both sides.

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

$\frac{{6} \times0.559}{5} =\sin B$

$0.6708=\sin B$

$\sin ^{-1}0.6708= B$

$42.1^\circ =B$

Switch the sides.

m∠B = 42.1°

Option A is the correct answer.