# How do you find the missing sides of a right triangle given a = ____, b = 24, c = 30?

May 19, 2015

Side $a = 18$ .

We will use the Pythagorean theorem: ${a}^{2} + {b}^{2} = {c}^{2}$.

a=?

b=24; b^2=24^2=576

c=30; c^2=30^2=900

Solve ${a}^{2} + {b}^{2} = {c}^{2}$ for ${a}^{2}$.

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

$900 - 576 = 324$

${a}^{2} = 324$

Take the square root of $324$ to find side $a$.

$a = \sqrt{{a}^{2}} = \sqrt{324} = 18$

May 21, 2015

Another simple way.
Ratio of the sides of right triangle: 3 : 4: 5
Ratio --> 18: 24: 30.
Then a = 18.