Question

find the length of side $x$ to the nearest tenth.
answer attempt 1 out of 2
$x = \square$
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Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. For the $30^\circ$ angle, opposite side is $x$, adjacent is 8.
$\tan(30^\circ) = \frac{x}{8}$

Step2: Solve for $x$

Rearrange to isolate $x$: $x = 8 \times \tan(30^\circ)$
$\tan(30^\circ) = \frac{\sqrt{3}}{3} \approx 0.577$
$x = 8 \times 0.577 \approx 4.616$

Step3: Round to nearest tenth

Round $4.616$ to one decimal place.
$x \approx 4.6$

Answer:

$4.6$