# How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 20, C= 25?

Mar 2, 2017

Missing side is $15$ or $32.02$ units

#### Explanation:

It is apparent that we are talking about a right angled triangle, whose two sides $A = 20$ and $C = 25$. In a right angled triangle, according to Pythagoras Theorem, square on the largest side, which is a hypotenuse, is equal to sum of the squares on other two sides.

Here we have two possibilities.

One - $C = 25$ is the hypotenuse and the largest side. As it's square is ${25}^{2} = 625$ and square of $A$ is ${20}^{2} = 400$, the square of third side would be $625 - 400 = 225$ and

third side, say $B = \sqrt{225} = 15$.

Two - $B$, the third side is the hypotenuse and the largest side. As sum of the square of other two sides $A$ and $C$ is ${20}^{2} = 400$ and ${25}^{2} = 625$, the square of third side $B$ would be $625 + 400 = 1025$ and

third side, $B = \sqrt{1025} \cong 32.02$.