Question

What is the length of leg y of the right triangle?

A right triangle with hypotenuse 85 and legs 84 and y

Answer 1

The length of leg y=13

Explanation:

Answer 2

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,

`(hypotenuse)^(2) = leg_(1)^(2)+leg_(2)^(2)`

As given in the question,

`hypotenuse = 85 \\\\leg_(1) = 84\\\\leg_(2) = y`

Put these values,

`\Rightarrow 85^(2)=84^(2) +y^(2) \\\\\Rightarrow y^(2)=85^(2)-84^(2)\\\\\Rightarrow y =\sqrt{85^(2)-84^(2)} \\\\\Rightarrow y =√(169)\\\\\Rightarrow y =13`

Hence, the length of leg y =13.