Question

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

Explanation:

Step1: Use tangent function

In right - triangle BCD, $\tan D=\frac{BC}{CD}$. Here, $D = 72^{\circ}$ and $CD = 13$, and $BC=x$. So $\tan72^{\circ}=\frac{x}{13}$.

Step2: Solve for x

We know that $\tan72^{\circ}\approx3.0777$. Then $x = 13\times\tan72^{\circ}$. Substituting the value of $\tan72^{\circ}$, we get $x=13\times3.0777 = 39.9101$.

Step3: Round to nearest tenth

Rounding $39.9101$ to the nearest tenth gives $x\approx39.9$.

Answer:

$39.9$