Question

which equation can be used to find the length of \\(\overline{ac}\\)?

(image of a right triangle with right angle at c, hypotenuse ab = 10 in, angle at b is 40°, side ac is labeled b, side bc is labeled a)

\\(\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 $\triangle ABC$, $\angle B=40^\circ$, hypotenuse $AB=10$ in, $\overline{AC}$ is opposite $\angle B$.

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