Solve triangles using the law of sines.

Question

asked Aug 8, 2021 151k views

2 Answers

Feliz · Answer 1 · 2021-08-13T16:52:34+0000

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

Explanation:

Using law of sines ∠B can be found using,

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

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,

$(\sin B)/(10)=(\sin 51^(\circ))/(11)$

Multiplying both sides by 10, we get,

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

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
$m \angle B=45$ °