Question

which equation can be used to find the length of $overline{ac}$?
(10)$\sin(40^{\circ}) = ac$
(10)$\cos(40^{\circ}) = ac$
$\frac{10}{\sin(40^{\circ})} = ac$
$\frac{10}{\cos(40^{\circ})} = ac$

Explanation:

Step1: Identify sides relative to $\angle B$

In right $\triangle ABC$, $\angle C=90^\circ$, hypotenuse $AB=10$ in. $\overline{AC}$ is the opposite side to $\angle B=40^\circ$.

Step2: Apply sine definition

Sine of an angle = $\frac{\text{Opposite}}{\text{Hypotenuse}}$. So $\sin(40^\circ)=\frac{AC}{10}$.

Step3: Rearrange to solve for $AC$

Multiply both sides by 10: $10\sin(40^\circ)=AC$.

Answer:

(10)$\sin(40^\circ)$ = AC