Advertisement Remove all ads

Advertisement Remove all ads

Advertisement Remove all ads

The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is

30 and that of the top of the flagstaff 60 . Find the height of the tower

[Use `sqrt(3)` 1.732 ]

Advertisement Remove all ads

#### Solution

Let AB be the tower and BC be the flagstaff,

We have,

BC = 6m, ∠AOB = 30° and ∠AOC - 60°

Let AB = h

In ΔAOB

`tan 30° = (AB)/(OA)`

`⇒ 1/ sqrt(3) = h/( OA)`

` ⇒ OA = h sqrt(3)` ..............(i)

Now in Δ AOC,

` tan 60° = (AC)/(OA)`

`⇒ sqrt(3) = (AB +BC)/ (h sqrt(3))` [ Using (i)]

⇒ 3h = h + 6

⇒ 3h - h = 6

⇒ 2h = 6

`⇒ h= 6/2`

⇒ h = 3m

So, the height of the tower is 3 m.

Concept: Heights and Distances

Is there an error in this question or solution?