A tower stands 50 meters tall. From its peak, the angles of depression to the top and bottom of a nearby building are measured at and , respectively. Determine the approximate height of the building as well as the horizontal distance separating the tower from the building.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Height = 21 m, Distance = 50 m.
Let building height = h, and distance between tower and building = x
From top of tower to bottom of building: tan45° = 50/x = 1 ⇒ x = 50 m
From top of tower to top of building: tan30° = (50 – h)/50
⇒ 50 – h = 50 × tan30° = 50 × (1/√3) ≈ 28.87
⇒ h = 50 – 28.87 = 21.13 ≈ 21 m