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

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Answer 1 · 2014-10-25T00:10:11

For this problem we have to use the Pythagorean Theorem.

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

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

${(2)}^{2} + b^{2} = {(24)}^{2}$ $(2)^2+b^2=(24)^2$

$b^{2} = {(24)}^{2} - {(2)}^{2}$ $b^2=(24)^2-(2)^2$

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

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

$b = \sqrt{576 - 4}$ $b=sqrt(576-4)$

$b = \sqrt{572}$ $b=sqrt(572)$

$b = \sqrt{4 \cdot 143}$ $b=sqrt(4*143)$

$b = 2 \sqrt{143}$ $b=2sqrt(143)$

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