which is the best approximation for the measure of angle egf?\n32.8°\n40.2°\n49.8°\n57.2°
which is the best approximation for the measure of angle egf?\n32.8°\n40.2°\n49.8°\n57.2°
Answer
Explanation:
Step1: Use sine - function definition
In right - triangle EFG with right - angle at E, $\sin(\angle EGF)=\frac{EF}{FG}$. Given $EF = 12$ in and $FG=18.6$ in, so $\sin(\angle EGF)=\frac{12}{18.6}$.
Step2: Calculate the sine value
$\frac{12}{18.6}\approx0.6452$.
Step3: Find the angle
We know that if $\sin\theta = 0.6452$, then $\theta=\sin^{- 1}(0.6452)$. Using a calculator, $\sin^{-1}(0.6452)\approx40.2^{\circ}$.
Answer:
$40.2^{\circ}$