2025 · Q25
A tower subtends an angle 60° at a point A on the same level as the foot of the tower. B is a point vertically above A and AB = h. The angle of depression of the foot of the tower, measured from B is 30°. What is the height of the tower ?
Elementary MathematicsTrigonometry
- A2h
- B2.5h
- C3h
- D3.5h
Explanation
Let the tower have height T and the point A be at ground distance d from its foot; then tan 60° = T/d. The point B is h above A, and the angle of depression of the foot from B is 30°, so tan 30° = h/d, giving d = h√3. Thus T = d√3 = 3h, option (c).