What is the length of b in a right triangle if a=2 and c=24?

Oct 25, 2014

For this problem we have to use the Pythagorean Theorem.

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

where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

${\left(2\right)}^{2} + {b}^{2} = {\left(24\right)}^{2}$

${b}^{2} = {\left(24\right)}^{2} - {\left(2\right)}^{2}$

$\sqrt{{b}^{2}} = \sqrt{{\left(24\right)}^{2} - {\left(2\right)}^{2}}$

$b = \sqrt{{\left(24\right)}^{2} - {\left(2\right)}^{2}}$

$b = \sqrt{576 - 4}$

$b = \sqrt{572}$

$b = \sqrt{4 \cdot 143}$

$b = 2 \sqrt{143}$