Question

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30° than when it was 45°. The height of the tower is ______.

Options

• `(2sqrt(3)x)` m

• `(3sqrt(2)x)` m

• `(sqrt(3) - 1)x` m

• `(sqrt(3) + 1)x` m

Answer 1

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30° than when it was 45°. The height of the tower is `underlinebb((sqrt(3) + 1)x  m)`.

Explanation:

Let h m be the height of the tower and let a m and (a + 2x) m be the lengths of the shadows of the tower when sun’s elevation is 45° and 30° respectively. 

Then, `h/a = tan 45^circ = 1` 

⇒ a = h

`h/(a + 2x) = tan 30^circ = 1/sqrt(3)`

⇒ `h/(h + 2x) = 1/sqrt(3)`

∴ `sqrt(3)h = h + 2x`

⇒ `2x = (sqrt(3) - 1)h`

⇒ `h = (2x)/((sqrt(3) - 1))`

∴ `h = {(2x)/((sqrt(3) - 1)) xx ((sqrt(3) + 1))/((sqrt(3) + 1))}`

= `x(sqrt(3) + 1)`