The difference between the heights of the building and the lamp-post.

32 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20 m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

28 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $20 m$
Let the height of the lamp post be h.
Let the distance between the foot of the lamp post and the foot of the tower be y.
Hence
$tan 30^{0} = \frac{1}{\sqrt{3}} = \frac{60 - h}{y}$
Hence
$y = \sqrt{3} (60 - h)$ ...(i)
And
$tan 60^{0} = \sqrt{3} = \frac{60}{y}$ ...(ii)
Hence
$y = 20 \sqrt{3}$
Hence
$20 \sqrt{3} = 60 \sqrt{3} - h \sqrt{3}$
$h = 40 m$
Hence difference in heights
$= 60 - 40 = 20 m$

Suggest Corrections

Similar questions

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp-post CD are observed to be $30^{\circ}$ and $60^{\circ}$ respectively. Find

(i) the horizontal distance between AB and CD,

(ii) the height of the lamp-post,

(iii) the difference between the heights of the building and the lamp-post.

Q. The horizontal distance between the building and the lamp-post

A body is projected from the top of a tower of height $32 m$ with a velocity of $20 m/s$ at an angle of $37^{\circ}$ above the horizontal. Find the velocity with which it hits the ground.

(Take $g = 10 m / s^{2}$ )

Q. From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 30° and 60° respectively. Find the height of the lamp post.

The distance between rooftops of two building of height 20 m and 41 m is 29 m. Find the horizontal distance between them.

Join BYJU'S Learning Program