Question

If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is `sqrt(3) : 1` then find the angle of elevation of the sun at that time.

Answer 1

Let AB be the pole and AC be its shadow.

Let AC = x, `AB = sqrt(3)x` and ∠ACB = θ.

Then,`(AB)/(AC) = tan θ`

⇒ `(sqrt(3)x)/x = tan θ`

⇒ `tan θ = sqrt(3)`

⇒ tan θ = 60°

⇒ θ = 60°