Question

From the diagram below, if the measure of < C = 30 °, and side AB = 13, then side AC = _____.

Answer 1

ANSWER:

b. 26

STEP-BY-STEP EXPLANATION:

We can determine the AC value, by means of the sine trigonometric function, which relates the opposite side to the angle and the hypotenuse, like this:

$\begin{gathered} \sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse}} \\ \\ \theta=\angle C=30\degree \\ \\ \text{ opposite = AB =13} \\ \\ \text{ hypotenuse = AC} \\ \\ \text{ We replacing:} \\ \\ \sin30\degree=\frac{13}{AC} \\ \\ AC=\frac{13}{\sin30\degree} \\ \\ AC=26 \end{gathered}$

So the correct answer is b. 26