13 in
Explanation
let's use the Pythagoras theorem
[tex]\text{side}^2+side^2=hyp^2[/tex]
then, let
adjancent side=side1=84 in
opposite side= y
hypotenuse=85 in
now, replace
[tex]\begin{gathered} 84^2+y^2=85^2 \\ 7056+y^2=7225 \\ \text{subtract 7056 in both sides} \\ 7056+y^2-7056=7225-7056 \\ y^2=169 \\ \sqrt[]{y}=\sqrt[]{169} \\ y=13 \end{gathered}[/tex]
so, the missing side is 13 in.
I hope this helps you
