Question

solve for x.
37°
8 m
x = ? m
round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\theta=37^\circ$, adjacent $=8$, opposite $=x$
$\tan(37^\circ)=\frac{x}{8}$

Step3: Solve for x

Rearrange to isolate $x$: $x=8\times\tan(37^\circ)$
Calculate $\tan(37^\circ)\approx0.7536$, so $x\approx8\times0.7536$

Step4: Compute final value

$x\approx6.0288$
Round to nearest hundredth: $x\approx6.03$

Answer:

$6.03$ m