Question

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

Step2: Apply sine definition

Sine of an angle = $\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(40^\circ) = \frac{AC}{10}$
Rearrange to solve for $AC$:
$10\sin(40^\circ) = AC$

Answer:

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