Option A:
m∠B = 42.1°
Solution:
Given data:
b = 18, c = 15 and m∠C = 34°
Using sine formula:
[tex]$\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Substitute the given values.
[tex]$\frac{18}{\sin B}=\frac{15}{\sin 34^\circ}[/tex]
Do cross multiplication.
[tex]${18} \times {\sin 34^\circ}={15} \times{\sin B}[/tex]
Divide by 15 on both sides.
[tex]$\frac{{18} \times {\sin 34^\circ}}{15} =\frac{{15} \times{\sin B}}{15}[/tex]
[tex]$\frac{{6} \times0.559}{5} =\sin B[/tex]
[tex]$0.6708=\sin B[/tex]
[tex]$\sin ^{-1}0.6708= B[/tex]
[tex]42.1^\circ =B[/tex]
Switch the sides.
m∠B = 42.1°
Option A is the correct answer.
