Answer
$a=12$ ft
Work Step by Step
RECALL:
The Pythagorean Theorem states that in a right triangle,
$c^2=a^2+b^2$
where
$c$ = length of the hypotenuse
$a$ and $b$ are the lengths of the two legs.
The given triangle has:
$b=5$ ft
$c=13$ ft
Use the Pythagorean Theorem above to obtain:
$c^2=a^2+b^2
\\13^2=a^2+5^2
\\169 = a^2 + 25
\\169 - 25=a^2
\\144=a^2$
Take the square root of both sides to obtain:
$\pm \sqrt{144} = a
\\\pm \sqrt{12^2} = a
\\\pm 12=a$
Note, however, that $a$ represents a length, so it cannot be negative.
Thus, $a=12$ ft.
