Question

The height of a house subtends a right angle at the opposite window. The angle of elevation of the window from the base of the house is 60°. If the width of the road is 6m, then find the height of the house?

Answer 1

See diagram. 

The answer is  8 √3 m.  It is simple from the diagram.

AB is the wall of the house.  D is the window on the opposite house CD.

CD = BC Tan 60° = 6√3 m  = BE

∠ ADE = ∠ADB - ∠EDB = 90° - ∠DBC = 30°

AE = DE tan 30 = 6 * 1/√3 = 2 √3 m

Hence the height of house AB = 8 √3 meters