Question

Find the value of $\tan 30°$ without using a calculator.

Answer 1

Calculate the value of $\tan 30°$.

Expand the expression in terms of sine and cosine.

$\begin{array}{rcl}\tan 30°& =& \frac{\sin 30°}{\cos 30°}\\ & =& \frac{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{{\displaystyle \raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\\ & =& \frac{1}{\sqrt{3}}\end{array}$

Hence, the required final answer is $\frac{1}{\sqrt{3}}$.