Answer
$tan(α) = \frac{\sqrt {3}}{2}$
$tan(β) = \frac{2}{\sqrt {3}}$
Work Step by Step
1. Find $AB$ using the Pythagorean Theorem
$a^{2} + b^{2} = c^{2}$
$(AB)^{2} + (\sqrt {3})^{2} = (\sqrt {7})^{2}$
$(AB)^{2} + 3 = 7$
$(AB)^{2} = 4$
$AB = \sqrt {4}$
$AB = 2$
2. Find $tan(α)$ (Recall that SOHCAHTOA, in this case we use TOA)
$tan = \frac{opposite}{adjacent}$
$tan(α) = \frac{\sqrt {3}}{2}$
2. Find $tan(β)$
$tan = \frac{opposite}{adjacent}$
$tan(β) = \frac{2}{\sqrt {3}}$
