Question

Find the length of the third side. If necessary, write in simplest radical form. 4 7

Answer 1

Using the Pythagorean Theorem :

`c^2=a^2+b^2`

Where c is the longest side or the hypotenuse

and

a and b are the legs of the right triangle

From the given figure,

The hypotenuse is 7 and one of the legs is 4

so c = 7 and a = 4

Using the formula above, solve for the value of the other leg.

`\begin{gathered} c^2=a^2+b^2 \\ 7^2=4^2+b^2 \\ 49=16+b^2 \\ 49-16=b^2 \\ b^2=33 \\ b=\sqrt[]{33} \end{gathered}`

Therefore, the third side is sq