Question

triangle abc is shown. what is sin(∠abc)? choose 1 answer: a 9√30 b 9√130 / 130 c 7√130 / 130 d 9 / 7

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle ABC$, the opposite side to $\angle ABC$ is $AC$ and the hypotenuse is $AB$.

Step2: Identify side lengths

We are given that $AC = 9$ and $AB=\sqrt{130}$.

Step3: Calculate sine value

$\sin(\angle ABC)=\frac{AC}{AB}=\frac{9}{\sqrt{130}}$. Rationalize the denominator: $\frac{9}{\sqrt{130}}\times\frac{\sqrt{130}}{\sqrt{130}}=\frac{9\sqrt{130}}{130}$.

Answer:

B. $\frac{9\sqrt{130}}{130}$