Question

solve for ( x ). round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

For $\angle E = 62^\circ$, side $CD=15$ is opposite, side $ED=x$ is adjacent. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(62^\circ) = \frac{15}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{15}{\tan(62^\circ)}$

Step4: Calculate value

$\tan(62^\circ) \approx 1.8807$, so $x \approx \frac{15}{1.8807} \approx 7.975$

Step5: Round to nearest tenth

$x \approx 8.0$

Answer:

$8.0$