In a right triangle, if c = 12 and b = 10, what is the length of a in simplified form?

Sep 1, 2016

As the hypotenuse: $a = 15.62$

As an arm, $a = 6.633$

Explanation:

It is not indicated whether a is the hypotenuse or one of the arms of the right-angle.

If a is the hypotenuse.

${a}^{2} = {12}^{2} + {10}^{2} = 144 + 100 = 244$

$a = \sqrt{244} = 15.62$

If a is not the hypotenuse:

${a}^{2} = {12}^{2} - {10}^{2} = 144 - 100 = 44$

$a = \sqrt{44} = 6.633$