Question

find the tangent of ∠d.
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\(\tan(d)=\\)

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle D$, the opposite side to $\angle D$ is $EF$ and the adjacent side is $DF$. First, find $DF$ using the Pythagorean theorem. Let $DF = x$. Then $x=\sqrt{DE^{2}-EF^{2}}$. Given $DE = 97$ and $EF = 72$, we have $x=\sqrt{97^{2}-72^{2}}=\sqrt{(97 + 72)(97 - 72)}=\sqrt{169\times25}=\sqrt{169}\times\sqrt{25}=13\times5 = 65$.

Step2: Calculate $\tan(D)$

$\tan(D)=\frac{EF}{DF}$. Since $EF = 72$ and $DF = 65$, then $\tan(D)=\frac{72}{65}$.

Answer:

$\frac{72}{65}$