Question

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

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. For $\angle H$ in right - triangle $HFG$, the opposite side to $\angle H$ is $FG$ and the adjacent side is $HF$.

Step2: Identify the lengths of the sides

We are given that $HF = 6$ and $FG=8$.

Step3: Calculate the tangent

$\tan(H)=\frac{FG}{HF}$. Substituting the values of $FG = 8$ and $HF = 6$, we get $\tan(H)=\frac{8}{6}$.

Step4: Simplify the fraction

$\frac{8}{6}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$