Question

from the top of the building of height 30m, the angle of depression of the top and bottom of another building of height h meters are 30° and 60° respectively. find h

Answer 1

The height of the another building, h is :

Given : height of the building = 30 cm, height of another building = h cm, angle of depression of the top = 30°, angle of depression of the bottom = 60°

• Suppose distance between two building is x

• In ∆ABC,

tan 30 = AB / BC = 30 - h / x

1/√3 = 30 - h / x

• x = 30√3 - √3h ....... 1

• In ∆ ADE,

tan 60 = AD / DE = 30 / x

√3 = 30 / x

• x = 30 / √3

Substitute value of x in equation 1

30 /√3 = 30√3 - h√3

30 = 30×3 - 3h

3h = 90 - 30 = 60

• h = 20 cm