Question

Hi plz help me with this geometry question

Answer 1

Answer:

Approximately 54°

Step-by-step explanation:

So we know Angle A, the side opposite to Angle A, and the side opposite to Angle B (the angle we want to find). Given these circumstances, we can use the Law of Sines.

The Law of Sines states that:

$\frac{\sin(A)}{a} =\frac{\sin(B)}{b} =\frac{\sin(C)}{c}$

The variables do not really matter. Instead, it's more important that the angle corresponding to the side lines up with each other.

Anyways, since we know Side A, Angle A, and Side B, let's use the first and second ratios:

$\frac{\sin(A)}{a} =\frac{\sin(B)}{b}$

Plug in 80° for A, 11 for a, and 9 for b:

$\frac{\sin(80)}{11} =\frac{\sin(B)}{9}$

Cross multiply to solve for B:

$9\sin(80)=11\sin(B)$

Divide both sides by 11:

$\sin(B)=\frac{9\sin(80)}{11}$

Use the inverse sine function. And finally, use a calculator to solve:

$\angle B =\sin^{-1}(\frac{9\sin(80)}{11} )\\\angle B\approx53.6829\textdegree\approx54\textdegree$