Question

What is the exact height of a right triangle with an angle that measures 30 degrees and a base of 8.

Answer 1

Given:

$\begin{gathered} \tan 30=\frac{AB}{BC} \\ \frac{1}{\sqrt[]{3}}=\frac{AB}{8} \\ AB=\frac{8}{\sqrt[]{3}} \\ AB=\frac{8}{3}\sqrt[]{3} \end{gathered}$

Height of the right triangle is

$\begin{gathered} AB=\frac{8}{3}\sqrt[]{3}\text{ units} \\ AB=4.6189\text{ units} \end{gathered}$