Question

From the top of a tower, the angle of depression of a boat is 30°. If the tower is 20 m high, how far is the boat from the foot of the tower? Leaving your answer in surd form with rational denominator

Answer 1

Given:-

The angle of depression of a boat is 30° and the tower is 20 m high.

Diagram:-

So from the figure, we need to find the value of BC.

So we use the formula,

$\tan \theta=\frac{opposite\text{ side}}{adjacent\text{ side}}$

Subsituting the value we get,

$\begin{gathered} \tan \theta=\frac{BC}{AC} \\ \tan 30=\frac{BC}{20} \\ \frac{1}{\sqrt[]{3}}=\frac{BC}{20} \\ BC=\frac{20}{\sqrt[]{3}} \end{gathered}$

So the required value is,

$\frac{20}{\sqrt[]{3}}$