Question

find gh.
7
23°
write your answer as an integer or as a decimal rounded to the nearest tenth.
gh =

Explanation:

Step1: Identify adjacent angle, side

In right $\triangle FGH$, $\angle G=23^\circ$, adjacent side $FG=7$, $GH$ is hypotenuse.

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(23^\circ)=\frac{FG}{GH}$
Rearrange to solve for $GH$: $GH=\frac{FG}{\cos(23^\circ)}$

Step3: Substitute values and calculate

Substitute $FG=7$, $\cos(23^\circ)\approx0.9205$:
$GH=\frac{7}{0.9205}\approx7.6$

Answer:

$7.6$