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

Explanation:

Step1: Identify similar - triangles

Since $EH\parallel FG$, $\triangle DEH\sim\triangle DFG$.

Step2: Use cosine definition in right - triangle

In right - triangle $\triangle DGH$, $\cos(G)=\frac{adjacent}{hypotenuse}$. First, find the hypotenuse of $\triangle DGH$. Using the Pythagorean theorem in $\triangle DGH$, if the two legs are $60$ and $63$, the hypotenuse $DG=\sqrt{60^{2}+63^{2}}=\sqrt{3600 + 3969}=\sqrt{7569}=87$. The adjacent side to $\angle G$ in right - triangle $\triangle DGH$ is $63$. So, $\cos(G)=\frac{63}{87}=\frac{21}{29}$.

Answer:

$\frac{21}{29}$