Question

In right triangle XYZ, the hypotenuse measures 14 inches and one leg measures 10 inches. Find the length of the other leg. Show your work and write your answer in simplest radical form.

Answer 1

As per given by the question,

There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.

Now,

First draw the triangle XYZ.

Now,

From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.

So,

First leg z is 10, then find the value of second leg x.

Then,

To find the value of second leg, here use pythagoras theorem.

So,

From the pythagoras theorem;

`XY^2+YZ^{2^{}^{}}=XZ^2`

Now,

`\begin{gathered} XY^2+YZ^2=XZ^2 \\ 10^2+x^2=14^2 \\ 100+x^2=196 \\ x^2=196-100 \\ x^2=96 \end{gathered}`

Then,

`\begin{gathered} x^2=96 \\ x=√(96)^{} \\ x=9.79 \end{gathered}`

Hence, the length of the other leg is 9.79.