find hi. write your answer as an integer or as a decimal rounded to the nearest tenth. hi =

Explanation:

Step1: Identify the trig - ratio

In right - triangle $HIJ$, we know the angle $\angle H = 52^{\circ}$ and the opposite side $IJ=\sqrt{59}$, and we want to find the adjacent side $HI$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan H=\frac{IJ}{HI}$.

Step2: Rearrange the formula

We can rewrite the formula $\tan H=\frac{IJ}{HI}$ as $HI = \frac{IJ}{\tan H}$.

Step3: Substitute the values

We know that $H = 52^{\circ}$ and $IJ=\sqrt{59}\approx7.681$. And $\tan52^{\circ}\approx1.2799$. Then $HI=\frac{\sqrt{59}}{\tan52^{\circ}}=\frac{7.681}{1.2799}\approx6.0$.

Answer:

$6.0$