## Thinking Mathematically (6th Edition)

$a=12$ cm.
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: $b=16$ cm $c=20$ cm Use the Pythagorean Theorem above to obtain: $c^2=a^2+b^2 \\20^2=a^2+16^2 \\400 = a^2 + 256 \\400-256=a^2 \\144=a^2$ 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, $a=12$ cm.