# How do you find the missing side of a right triangle given a = ?, b = 9, c = 16?

##### 1 Answer

Apply the pythagorean theorem to get

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

${a}^{2} + {9}^{2} = {16}^{2}$

${a}^{2} = 256 - 81 = 175$

$a = \pm \sqrt{175}$

Hence $a > 0$ then $a = 5 \sqrt{7} \approx 13.23$

Also a could be the hypotenuse in the triangle hence

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

${a}^{2} = {9}^{2} + {16}^{2}$

$a \approx 18.36$