#### Answer

a=4.5

#### Work Step by Step

The Pythagorean Theorem states that for a right triangle, $a^{2} +b^{2} = c^{2}$. Thus, we plug in the values given for a, b, or c, and then we use these values to find the missing value:
$a^{2} + 6^{2} =7.5^{2} \\\\ a^{2} + 36=56.25 \\\\ a^{2} =20.25 \\\\ a=4.5$