Question

a triangle was dilated by a scale factor of 4. if tan a° = $\frac{4}{3}$ and $overline{fd}$ measures 12 units, how long is $overline{ef}$?
$overline{ef}=6$ units
$overline{ef}=9$ units
$overline{ef}=12$ units
$overline{ef}=16$ units

Explanation:

Step1: Recall tangent definition

In a right - triangle, $\tan\alpha=\frac{\text{opposite}}{\text{adjacent}}$. Let $\overline{FD}$ be the adjacent side to angle $\alpha$ and $\overline{EF}$ be the opposite side to angle $\alpha$. Given $\tan\alpha = \frac{4}{3}=\frac{\overline{EF}}{\overline{FD}}$.

Step2: Substitute the value of $\overline{FD}$

We know that $\overline{FD} = 12$ units. Substituting into $\tan\alpha=\frac{\overline{EF}}{\overline{FD}}$, we get $\frac{4}{3}=\frac{\overline{EF}}{12}$.

Step3: Solve for $\overline{EF}$

Cross - multiply: $3\times\overline{EF}=4\times12$. Then $3\times\overline{EF} = 48$. Divide both sides by 3: $\overline{EF}=\frac{48}{3}=16$ units.

Answer:

$\overline{EF}=16$ units