Question

If the height of a vertical pole is 3–√3 times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is
(A) 30°
(B) 60°
(C) 45°
(D) 75°

Answer 1

Let AO be the pole and OB be its shadow.
Let the length of the shadow be x.
Let θ be the angle of elevation of the Sun at that time.
Given:
Height of pole (h) =\[\sqrt{3} \times\] Length of its shadow

\[\Rightarrow h = \sqrt{3}x\]

We have:

\[\tan \theta = \frac{AO}{OB}\]

\[ = \frac{h}{x}\]

\[ = \frac{\sqrt{3}x}{x}\]

\[ = \sqrt{3}\]

\[ \Rightarrow \tan \theta = \tan 60^o\]

\[ \Rightarrow \theta = {60}^\circ\]

Thus, the angle of elevation of the Sun is 60°.
Hence, the correct option is B.