which is the best approximation for the measure of angle egf? 32.8° 40.2° 49.8° 57.2°

Explanation:

Step1: Identify trig - function

In right - triangle EFG with right - angle at E, we know the opposite side (EF = 12 in.) and the hypotenuse (FG = 18.6 in.) with respect to angle EGF. We use the sine function, $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(\angle EGF)=\frac{EF}{FG}=\frac{12}{18.6}$.

Step2: Calculate the sine value

$\frac{12}{18.6}\approx0.6452$.

Step3: Find the angle

We know that if $\sin(x)=a$, then $x = \sin^{- 1}(a)$. So, $\angle EGF=\sin^{-1}(0.6452)$. Using a calculator, $\sin^{-1}(0.6452)\approx40.2^{\circ}$.

Answer:

$40.2^{\circ}$