Question

From the top of a building AB, 60 m high, the angles of depression of the top and bottom at a vertical lamp post CD are observed to have measure 30 and 60 respectively. Find,
(1) the horizontal distance between building and lamp post.
(2) the height of the lamp post.
(3) the difference between the heights of the building and the lamp post.

Answer 1

Let the distance between tower and building be "d".

Acc to the question,

tan 30° = (60 - height of tower) / d

tan 60° = 60 / d

or, d = 60/√3.

Putting the value of d we get,

tan 30° = (60 - height of tower) / 60/√3.

or, 1/√3 = (60 - height of tower) / 60/√3

or, 60/3 = (60 - height of tower)

or, Height of tower = 60 - 20 = 40.

Therefore,

(1) the horizontal distance between building and lamp post = 60/√3 m.

(2) the height of the lamp post = 40 m.

(3) the difference between the heights of the building and the lamp post = 60 - 40 = 20 m.