#### Answer

$a\approx13.2\text{ or }a\approx-13.2$

#### Work Step by Step

We start with the given equation: $20^2=15^2+a^2$
To simplify each of the constants being squared, we multiply them by themselves: $400=225+a^2$
In order to get the term with $a$ by itself, we subtract $225$ from both sides of the equation: $$400-225=225-225+a^2$$$$175=a^2$$
To solve the equation $175=a^2$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$175=a^2$$$$\sqrt {175}=\sqrt {a^2}$$$$a\approx\pm13.2$$$$a\approx13.2\text{ or }a\approx-13.2$$