From a point A on the ground, the angle of elevation to the top of a building is 30°. From a point B, which is directly between A and the foot of the building, the angle of elevation is 60°. What is the ratio of the distance of point A from the building's foot to the distance of point B from the building's foot?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 3 : 1.
Let the foot of the building at the point O, and the height of the building = h
From point A: tan30° = h/OA
⇒ 1/√3 = h/OA
⇒ OA = h√3
From point B: tan60° = h/OB
⇒ √3 = h/OB
⇒ OB = h/√3
OA : OB = (h√3) : (h/√3) = √3 : (1/√3) = 3 : 1