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, for an acute angle $\theta$, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle H$ in right - triangle $GHI$ with right - angle at $G$, the side opposite $\angle H$ is $GI$ and the side adjacent to $\angle H$ is $GH$.

Step2: Identify the lengths of the opposite and adjacent sides

We are given that $GH = 24$ and $GI=70$.

Step3: Calculate the tangent of $\angle H$

$\tan(H)=\frac{GI}{GH}=\frac{70}{24}$.

Step4: Simplify the fraction

$\frac{70}{24}=\frac{35}{12}$.

Answer:

$\frac{35}{12}$