Question

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

Answer 1

`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 = 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)`