Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

Question: Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

Question:

Let the height of the second building AD be h.
EC = 100 - h
DC = AB = 40

here,
EC/DC = tan60°
⇒ (100 - h)/40 = √3
⇒ 100 - h = 40√3
⇒ h = 100 - 69.2
∴ h = 30.8