Question

If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then the Sun's elevation 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 = 6 m and BC = $2\sqrt{3}$ m

In right ∆ABC,

$$\begin{gathered} \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{6\mathrm{m}}{2\sqrt{3}\mathrm{m}} \\ \Rightarrow \tan \theta =\sqrt{3} \end{gathered}$$
$$\begin{gathered} \Rightarrow \tan \theta =\tan 60° \\ \Rightarrow \theta =60° \end{gathered}$$

Hence, the Sun's elevation is 60º.

If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then the Sun's elevation is ___60º___.