find the sine of ∠e. 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 $\angle E$, the side opposite to $\angle E$ is $FG$ and the hypotenuse is $EG$.

Step2: Identify side lengths

We are given that $FG = 72$ and $EG=90$.

Step3: Calculate $\sin(E)$

$\sin(E)=\frac{FG}{EG}=\frac{72}{90}$.

Step4: Simplify the fraction

$\frac{72}{90}=\frac{72\div18}{90\div18}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$