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

##### 1 Answer

Jul 8, 2017

#### Explanation:

Pythagoras' theorem tells us that the square of the length of the hypotenuse (

That is:

#c^2 = a^2+b^2#

So in our example:

#c^2 = color(blue)(20)^2+color(blue)(21)^2 = 400+441 = 841 = color(blue)(29)^2#

Hence:

#c = 29#

Pythagoras' formula is equivalent to:

#c = sqrt(a^2+b^2)#

and:

#a = sqrt(c^2-b^2)#