#### Answer

$a\approx 10.2$ cm

#### Work Step by Step

RECALL:
The Pythagorean Theorem states that in a right triangle,
$c^2=a^2+b^2$
where:
$a$ and $b$ are the lengths of the legs (non-hypotenuse sides)
$c$ is the length of the hypotenuse
Use the Pythagorean Theorem with c = 15 and b = 11 to obtain:
$15^2 = a^2 + 11^2
\\225=a^2+121
\\225-121=a^2
\\104=a^2$
Take the square root of both sides to obtain:
$\pm \sqrt{104} = a$
Use a scientific calculator to obtain:
$\pm 10.19803903 = a
\\\pm 10.2 \approx a$
Since $a$ represents a length, it cannot be negative.
Thus,
$a\approx 10.2$ cm