Question

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

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle F$ in right - triangle $GHF$, the side opposite $\angle F$ is $GH$ and the side adjacent to $\angle F$ is $HF$.

Step2: Use the Pythagorean theorem to find $GH$

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 17$ (hypotenuse) and $b = 8$ (one leg). Let $a=GH$. Then $a=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$.

Step3: Calculate $\tan(F)$

$\tan(F)=\frac{GH}{HF}$. Since $GH = 15$ and $HF = 8$, $\tan(F)=\frac{15}{8}$.

Answer:

$\frac{15}{8}$