find m∠g.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠g = □°

Explanation:

Step1: Recall trigonometric ratio

We use the tangent - inverse function. In right - triangle $HFG$ with right - angle at $F$, $\tan G=\frac{opposite}{adjacent}=\frac{HF}{FG}$.

Step2: Identify the sides

We know that $HF$ is the side opposite to $\angle G$ and $FG$ is the side adjacent to $\angle G$. Given $HF = 7$ and $FG=9$.

Step3: Calculate the tangent of $\angle G$

$\tan G=\frac{7}{9}\approx0.7778$.

Step4: Find the measure of $\angle G$

$m\angle G=\arctan(\frac{7}{9})$. Using a calculator in degree mode, $m\angle G=\arctan(0.7778)\approx37.9^{\circ}$.

Answer:

$37.9$