#### Answer

$\tan\alpha=\frac{15}{8}$
$\tan\beta=\frac{8}{15}$

#### Work Step by Step

Let $x$ be the side of the triangle with an unknown length.
Using Pythagorean Theorem to find $x$.
$x=\sqrt{17^{2}-15^{2}}$
$x=8$
$\tan\alpha=\frac{opposite}{hypotenuse}=\frac{15}{x}=\frac{15}{8}$
$\tan\beta=\frac{opposite}{hypotenuse}=\frac{x}{15}=\frac{8}{15}$