find the sine of ∠u. simplify your answer and write it as a proper fraction, improper fraction, or whole…

Explanation:

Step1: Recall sine - ratio definition

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

Step2: Find the length of the opposite side

First, use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ to find the length of $WV$. Let $a = 65$ and $c = 97$. Then $WV=\sqrt{97^{2}-65^{2}}=\sqrt{(97 + 65)(97 - 65)}=\sqrt{162\times32}=\sqrt{5184}=72$.

Step3: Calculate $\sin(U)$

$\sin(U)=\frac{WV}{WU}$. Since $WV = 72$ and $WU=97$, then $\sin(U)=\frac{72}{97}$.

Answer:

$\frac{72}{97}$