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 ______.

Options

• 7.5 m

• 15 m

• `10sqrt(3)` m

• `5sqrt(3)` m

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 AB be the pole and AC and AD be its shadows when ∠ACB = 30° and ∠ADB = 60°.

From right ΔCAB, we have

`(AC)/(AB) = cot 30^circ`

⇒ `(AC)/(15  m) = sqrt(3)`

⇒ `AC = 15sqrt(3)  m`   ...(i)

From right ΔDAB, we have

`(AD)/(AB) = cot 60^circ`

⇒ `(AD)/(15  m) = 1/sqrt(3)`

⇒ `AD = (15  m)/sqrt(3)`

⇒ `AD = (15  m)/sqrt(3) xx sqrt(3)/sqrt(3)`

⇒ `AD = 5sqrt(3)  m`   ...(ii)

∴ Required difference = `(15sqrt(3) - 5sqrt(3)) m`

= `10sqrt(3)  m`