Question

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

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Calculate the sine value

$\sin(x)=\frac{12}{18.6}\approx0.6452$.

Step3: Find the angle

We use the inverse - sine function $x = \sin^{-1}(0.6452)$. Using a calculator, $x=\sin^{-1}(0.6452)\approx40.2^{\circ}$.

Answer:

$40.2^{\circ}$