Question

Solve triangles using the law of sines.

Answer 1

The measure of angle B is $m \angle B=45$°

Step-by-step explanation:

Using law of sines ∠B can be found using,

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

where b,c denotes the side and B,C denotes the angle.

Also, it is given that $b=10$, $c=11$ and ∠C=51°.

To find ∠B, let us substitute the values in this formula, we get,

$\frac{\sin B}{10}=\frac{\sin 51^{\circ}}{11}$

Multiplying both sides by 10, we get,

$\begin{aligned}\sin B &=\frac{10}{11} \sin 51^{\circ} \\&=\frac{10}{11}(0.7771) \\&=\frac{7.771}{11} \\\sin B &=0.7065\end{aligned}$

Taking $\sin ^{-1}$ on both sides,

$\begin{aligned}&B=\sin ^{-1}(0.7065)\\&B=44.95^{\circ}\end{aligned}$

Rounding it off to the nearest degree,we get,

$m \angle B=45$

Thus, the measure of angle B is $m \angle B=45$°

Answer 2

Answer:

Measure of angle A

Step-by-step explanation: