Question

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

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 34^\circ$, opposite side $HI = 4$, adjacent side $GH$ is unknown.

Step2: Rearrange to solve for GH

$\tan(34^\circ) = \frac{4}{GH} \implies GH = \frac{4}{\tan(34^\circ)}$

Step3: Calculate the value

$\tan(34^\circ) \approx 0.6745$, so $GH \approx \frac{4}{0.6745} \approx 5.9$

Answer:

$5.9$