Question

triangle abc is shown. what is sin(∠bac)? choose 1 answer. a 9√106 / 106 b 9 / 106 c 5√106 / 106

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle BAC$, the opposite side to $\angle BAC$ is $BC = 9$ and the hypotenuse is $AB=\sqrt{106}$.

Step2: Calculate $\sin(\angle BAC)$

$\sin(\angle BAC)=\frac{BC}{AB}=\frac{9}{\sqrt{106}}=\frac{9\sqrt{106}}{106}$.

Answer:

B. $\frac{9\sqrt{106}}{106}$