find the tangent of ∠h. simplify your answer and write it as a proper fraction, improper fraction, or whole…

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle H$, the opposite side is $IJ$ and the adjacent side is $HI$.

Step2: Identify the lengths of the opposite and adjacent sides

We are given that $IJ = 24$ (opposite to $\angle H$) and $HI=10$ (adjacent to $\angle H$).

Step3: Calculate the tangent of $\angle H$

$\tan(H)=\frac{IJ}{HI}=\frac{24}{10}$.

Step4: Simplify the fraction

$\frac{24}{10}=\frac{12}{5}$.

Answer:

$\frac{12}{5}$