# Using the pythagorean theorem, how do you solve for the missing side given a = 20 and b = 21?

Jul 8, 2017

$c = 29$

#### Explanation:

Pythagoras' theorem tells us that the square of the length of the hypotenuse ($c$) of a right angled triangle is the sum of the squares of the lengths of the other two sides ($a$ and $b$).

That is:

${c}^{2} = {a}^{2} + {b}^{2}$

So in our example:

${c}^{2} = {\textcolor{b l u e}{20}}^{2} + {\textcolor{b l u e}{21}}^{2} = 400 + 441 = 841 = {\textcolor{b l u e}{29}}^{2}$

Hence:

$c = 29$

Pythagoras' formula is equivalent to:

$c = \sqrt{{a}^{2} + {b}^{2}}$

and:

$a = \sqrt{{c}^{2} - {b}^{2}}$