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

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle H$, the adjacent side to $\angle H$ is $HG = 39$, and we first need to find the hypotenuse $FH$.

Step2: Use the Pythagorean theorem to find the hypotenuse

In right - triangle $FGH$ with legs $FG$ and $HG$, by the Pythagorean theorem $FH^{2}=FG^{2}+HG^{2}$. Given $FG = 80$ and $HG = 39$, then $FH=\sqrt{80^{2}+39^{2}}=\sqrt{6400 + 1521}=\sqrt{7921}=89$.

Step3: Calculate $\cos(H)$

Using the cosine ratio $\cos(H)=\frac{HG}{FH}$. Since $HG = 39$ and $FH = 89$, then $\cos(H)=\frac{39}{89}$.

Answer:

$\frac{39}{89}$