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?
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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
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
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