Answer
$\tan\alpha=\frac{\sqrt5}{2}$
$\tan\beta=\frac{2}{\sqrt5}$
Work Step by Step
Let $x$ be the side of the triangle with an unknown length.
Using Pythagorean Theorem to find $x$.
$x=\sqrt{6^{2}-4^{2}}$
$x=\sqrt{20}$
$x=2\sqrt5$
$\tan\alpha=\frac{opposite}{hypotenuse}=\frac{x}{4}=\frac{2\sqrt5}{4}=\frac{\sqrt5}{2}$
$\tan\beta=\frac{opposite}{hypotenuse}=\frac{4}{x}=\frac{4}{2\sqrt5}=\frac{2}{\sqrt5}$
