Question

in △def, the measure of ∠f = 90°, df = 8, fe = 15, and ed = 17. what ratio represents the tangent of ∠d?

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For $\angle D$ in right - triangle $\triangle DEF$ with $\angle F = 90^{\circ}$, the opposite side to $\angle D$ is $FE$ and the adjacent side is $DF$.

Step2: Calculate the tangent ratio

The formula for $\tan D=\frac{\text{opposite}}{\text{adjacent}}$. Given $DF = 8$ and $FE = 15$, then $\tan D=\frac{FE}{DF}=\frac{15}{8}$.

Answer:

$\frac{15}{8}$