Question

find the sine of ∠q.
simplify your answer and write it as a proper fraction, number.
sin(q) =

Explanation:

Step1: Recall sine - definition

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

Step2: Identify side lengths

We know that the side opposite to $\angle Q$ has length $32$ and the hypotenuse has length $68$.

Step3: Calculate sine value

$\sin(Q)=\frac{32}{68}$.

Step4: Simplify the fraction

$\frac{32}{68}=\frac{8}{17}$ (divide both numerator and denominator by 4).

Answer:

$\frac{8}{17}$