find hi.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nhi = \nsubmit

Explanation:

Step1: Recall tangent function in right - triangle

In right - triangle $\triangle GHI$ with $\angle I = 90^{\circ}$, $\tan H=\frac{GI}{HI}$. We know that $GI = \sqrt{10}$ and $\angle H=35^{\circ}$. So, $\tan35^{\circ}=\frac{\sqrt{10}}{HI}$.

Step2: Solve for $HI$

We can rewrite the equation as $HI=\frac{\sqrt{10}}{\tan35^{\circ}}$. Since $\tan35^{\circ}\approx0.7002$ and $\sqrt{10}\approx3.1623$, then $HI=\frac{3.1623}{0.7002}\approx4.5$.

Answer:

$4.5$