Answer
$\dfrac{\sqrt{3}}{3}$
Work Step by Step
RECALL:
(1) $\sin{\theta} = \dfrac{\text{opposite side}}{\text{hypotenuse}}$
(2) $\tan{\theta} = \dfrac{\text{opposite side}}{\text{adjacent side}}$
(3) $\cos{\theta} = \dfrac{\text{adjacent side}}{\text{hypotenuse}}$
Use formula (1) above.
Use the 30-degree angle of the triangle on the right to obtain:
$\tan{30^o} = \dfrac{1}{\sqrt3}$
Rationalize the denominator by multiplying $\sqrt{3}$ to both the numerator and the denominator to obtain
$\tan{30^o}=\dfrac{ 1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}
\\\tan{30^o}=\dfrac{\sqrt{3}}{3}.$
