Question

If the height of a vertical pole is `sqrt(3)` times the length of its shadow on the ground then the angle of elevation of the sun at that time is ______.

Options

• 30°

• 45°

• 60°

• 75°

Answer 1

If the height of a vertical pole is `sqrt(3)` times the length of its shadow on the ground then the angle of elevation of the sun at that time is 60°.

Explanation:

Let AB be the pole and AC be its shadow.

Let AC = x m.

Then, `AB = sqrt(3)x  m`.

Let ∠ACB = θ.

Then, `tan θ = (AB)/(AC)`

= `(sqrt(3)x)/x`

= `sqrt(3)`

= tan 60°

⇒ θ = 60°