Question

find m∠g.

write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠g = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle GEF \) with \( \angle E = 90^\circ \), hypotenuse \( GF = 6.6 \), and opposite side to \( \angle G \) is \( EF = 4.8 \). We use the sine function: \( \sin(\angle G)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{EF}{GF} \).

Step2: Calculate the sine value

Substitute the values: \( \sin(\angle G)=\frac{4.8}{6.6}\approx0.7273 \).

Step3: Find the angle

Take the inverse sine: \( \angle G=\sin^{-1}(0.7273) \). Using a calculator, \( \angle G\approx46.7^\circ \) (rounded to the nearest tenth).

Answer:

\( 46.7 \)