Question

find m∠e. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠e = 。

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle $DEF$ with right - angle at $D$, we know the opposite side ($DF = 8.9$) and the hypotenuse ($EF=10.2$) with respect to angle $E$. We use the sine ratio, $\sin E=\frac{opposite}{hypotenuse}$.
So, $\sin E=\frac{DF}{EF}=\frac{8.9}{10.2}$.

Step2: Calculate the value of $\sin E$

$\sin E=\frac{8.9}{10.2}\approx0.8725$.

Step3: Find the measure of angle $E$

We know that if $\sin E = x$, then $E=\sin^{- 1}(x)$. So, $E=\sin^{-1}(0.8725)$.
Using a calculator, $E\approx60.8^{\circ}$.

Answer:

$60.8$