Question

triangle abc is shown. what is sin(∠abc)? choose 1 answer: a $\frac{5sqrt{74}}{74}$ b $7sqrt{74}$ c $\frac{7sqrt{74}}{74}$ d $\frac{7}{}$

Explanation:

Step1: Recall sine - definition

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle ABC$

For $\angle ABC$, opposite side is $AC = 7$, hypotenuse is $AB=\sqrt{74}$

Step3: Calculate sine value

$\sin(\angle ABC)=\frac{7}{\sqrt{74}}=\frac{7\sqrt{74}}{74}$

Answer:

C. $\frac{7\sqrt{74}}{74}$