# How do you find the missing side of a right triangle given: b=24, c=26?

Dec 21, 2016

$a = 10$

#### Explanation:

Assuming that the sides are $a , b , c$ with $c$ being the hypotenuse, we can use the pythagorean triples to find the third and shortest side.

Some of the common triples and their multiples are:

$3 : 4 : 5 \rightarrow \text{ "6:8:10" "9:12:15" } 12 : 16 : 20$
$5 : 12 : 13 \rightarrow \text{ "color(red)(10:24:26)" } 15 : 36 : 39$
$7 : 24 : 25 \rightarrow \text{ } 14 : 48 : 50$
$8 : 15 : 17 \rightarrow \text{ } 16 : 30 : 34$

$\textcolor{red}{10 : 24 : 26}$ is what we want. The third side is $10$

We could also calculate the unknown side

${a}^{2} = {26}^{2} - {24}^{2}$

${a}^{2} = 676 - 576 = 100$

$a = \sqrt{100} = 10$