Question

The angle of elevation of the sun when the shadow of a pole h meter high is $\sqrt{3}h$ meters long is __________.

Answer 1

Let the angle of elevation of Sun be θ.



Here, AB is the pole and BC is the shadow of the pole.

AB = h m and BC = $\sqrt{3}h$ m

In right ∆ABC,

$$\begin{gathered} \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{h\mathrm{m}}{\sqrt{3}h\mathrm{m}} \\ \Rightarrow \tan \theta =\frac{1}{\sqrt{3}} \end{gathered}$$
$$\begin{gathered} \Rightarrow \tan \theta =\tan 30° \\ \Rightarrow \theta =30° \end{gathered}$$

Hence, the angle of elevation of Sun is 30º.

The angle of elevation of the sun when the shadow of a pole h meter high is $\sqrt{3}h$ meters long is ____30º____.