Question

If the elevation of the sun changes from 30° to 60°, then the difference between the lengths of shadows of a pole 15 m high is ______.

Answer 1

If the elevation of the sun changes from 30° to 60°, then the difference between the lengths of shadows of a pole 15 m high is `underlinebb(10sqrt(3)  m)`.

Explanation:

Let h = 15 m. Shadow length = h cot θ.

For θ = 30°,

cot 30° = `sqrt(3)`

⇒ Shadow = `15·sqrt(3)`.

For θ = 60°,

cot 60° = `1/sqrt(3)`

⇒ Shadow = `15/sqrt(3)`

= `5sqrt(3)` 

Difference = `15sqrt(3) - 5sqrt(3)`

= `10sqrt(3)` m