# How do you find the missing sides of a right triangle given a = 5, b = 3, c = ____?

May 9, 2015

c = 4.

Reminder: The ratio of the sides of a right triangle: 3:4:5.

May 9, 2015

Which side is the hypotenuse?
If the hypotenuse is $c$, then use

${a}^{2} + {b}^{2} = {c}^{2}$ to get:

${5}^{2} + {3}^{2} = {c}^{2}$, so ${c}^{2} = 34$ abd

$c = \sqrt{34}$

If the hypotenuse is $a$, then use

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

In this case, we get

${3}^{2} + {c}^{2} = {5}^{2}$, so that

${c}^{2} = 25 - 9 = 16$ and so,

$c = \sqrt{16} = 4$.