use the information given in the figure to find the length eh. if applicable, round your answer to the…

Explanation:

Step1: Apply Pythagorean theorem in right - triangle FHG

In right - triangle $FHG$, by the Pythagorean theorem $FH^{2}+HG^{2}=FG^{2}$. We know $FG = 85$ and $HG=77$. So, $FH=\sqrt{FG^{2}-HG^{2}}$. $FH=\sqrt{85^{2}-77^{2}}=\sqrt{(85 + 77)(85 - 77)}=\sqrt{162\times8}=\sqrt{1296}=36$.

Step2: Apply Pythagorean theorem in right - triangle EFH

In right - triangle $EFH$, by the Pythagorean theorem $EH^{2}+FH^{2}=EF^{2}$. We know $EF = 45$ and $FH = 36$. So, $EH=\sqrt{EF^{2}-FH^{2}}$. $EH=\sqrt{45^{2}-36^{2}}=\sqrt{(45 + 36)(45 - 36)}=\sqrt{81\times9}=\sqrt{729}=27$.

Answer:

27