If the elevation of the sun changed from 30° to 60°, then the difference between the lengths of shadows of a pole 15 m high, made at these two positions is:

1. 7.5 m

2. 15 m

3. $5\sqrt{3}$ m

4. $10\sqrt{3}$ m

Height of pole AB = 15 m

Let D be the position where angle of elevation is 30° and C be the point where angle of elevation is 60°.

In triangle ABC,

We know that,

$\Rightarrow \tan 60^{\circ} = \dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AB}{BC} \\[1em] \Rightarrow \sqrt3 = \dfrac{15}{BC} \\[1em] \Rightarrow BC = \dfrac{15}{\sqrt3} \\[1em] \Rightarrow BC = \dfrac{15}{\sqrt{3}} \times \dfrac{\sqrt3}{\sqrt3} \\[1em] \Rightarrow BC = \dfrac{15\sqrt3}{3} \\[1em] \Rightarrow BC = 5\sqrt3 \text{ m.}$

In triangle ABD,

We know that,

$\Rightarrow \tan 30^{\circ} = \dfrac{\text{Perpendiuclar}}{\text{Base}} = \dfrac{AB}{BD} \\[1em] \Rightarrow \dfrac{1}{\sqrt3} = \dfrac{15}{BD} \\[1em] \Rightarrow BD = 15\sqrt3 \text{ m.}$

From figure,

CD = BD - BC

CD = $15\sqrt3 - 5\sqrt3$

CD = $10\sqrt3 \text{ m.}$

Hence, option 4 is the correct option.