Question

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

Options

• `sqrt(3)` b

• `"b"/3`

• `"b"/2`

• `"b"/sqrt(3)`

Answer 1

`"b"/2`

Explanation;

Hint:

Let the height of the pole BC be h

AC = b + h

Let CD be x

In the right ∆BCD, tan 30° = `"BC"/"AB"`

`1/sqrt(3)= "h"/x`

x = `sqrt(3)`h  ...(1)

In the right ∆ACD, tan 60° = `"AC"/"CD"`

`sqrt(3) = ("b" + "h")/x`

x = `("b" + "h")/sqrt3` ....(2)

From (1) and (2) we get

`sqrt(3)`h = `("b" + "h")/sqrt(3)`

 ⇒ 3h = b + h

2h = b

⇒ h = `"b"/2`