Question

question
solve for $x$. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 26^\circ$, opposite side to $\angle H$ is $FG$, adjacent side is $GH = x$, and hypotenuse $FH=47$. First find $FG$ using sine, then use tangent for $x$.
Alternatively, use cosine directly: $\cos(H) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{47}$

Step2: Rearrange to solve for $x$

$x = 47 \times \cos(26^\circ)$

Step3: Calculate the value

First, $\cos(26^\circ) \approx 0.8988$, then $x \approx 47 \times 0.8988$
$x \approx 42.2436$

Step4: Round to nearest tenth

$x \approx 42.2$

Answer:

$42.2$