Solution :
Given a right triangle with hypotenuse 85 and legs 84 and y.
Use Pythagoras theorem, to find the length of the leg y of the right triangle.
According to Pythagoras theorem,
[tex](hypotenuse)^{2} = leg_{1}^{2}+leg_{2}^{2}[/tex]
As given in the question,
[tex]hypotenuse = 85 \\\\leg_{1} = 84\\\\leg_{2} = y[/tex]
Put these values,
[tex]\Rightarrow 85^{2}=84^{2} +y^{2} \\\\\Rightarrow y^{2}=85^{2}-84^{2}\\\\\Rightarrow y =\sqrt{85^{2}-84^{2}} \\\\\Rightarrow y =\sqrt{169}\\\\\Rightarrow y =13[/tex]
Hence, the length of leg y =13.
