How do you find the missing length for the right triangle below the short side is 9cm and the hypotenuse is 30 cm?

Apr 21, 2016

28.62cm

Explanation:

The Pythagorean theorem is this: ${a}^{2} + {b}^{2} = {c}^{2}$, where $c$ is the hypotenuse (which is the longest side and is opposite the right angle), and $a$ and $b$ are the other sides. Given the information we have, we can say that:
${9}^{2} + {b}^{2} = {30}^{2}$, where $b$ is the unknown side.
Now its a matter of rearranging and solving:
${b}^{2} = {30}^{2} - {9}^{2}$
${b}^{2} = 900 - 81$
${b}^{2} = 819$
$b = \sqrt{28.618}$
And if you type that into your calculator you'll get $b = 28.62 c m$ (Don't forget units)