Question

Use the law of sines to find m

Answer 1

Answer: 5.22

Step-by-step explanation:

Given

$\angle A=103^{\circ}$

Sine law is    $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Here, a=8, c=5

Putting values

$\Rightarrow \dfrac{8}{\sin 103}=\dfrac{5}{\sin C}\\\\\Rightarrow \sin C=\dfrac{5}{8}\sin 103^{\circ}=0.6089\\\Rightarrow C=37.51^{\circ}$

$\Rightarrow \angle B=180^{\circ} -103^{\circ}-37.51^{\circ}\\\Rightarrow \angle B=39.49^{\circ}$

If b=m, then

$\Rightarrow \dfrac{8}{\sin 103^{\circ}}=\dfrac{m}{\sin 39.49^{\circ}}\\\\\Rightarrow m=\dfrac{\sin 39.49^{\circ}}{\sin 103^{\circ}}\times 8=5.22$