2026 · Q45
A tower subtends an angle α at a point P on the same level as the foot of the tower. Q is a point vertically above P and PQ = h. If the angle of depression of the foot of the tower measured from Q is β, then what is the height of the tower?
Elementary MathematicsTrigonometry
- Ah tanα tanβ
- Bh cotα tanβ
- Ch tanα cotβ
- Dh cotα cotβ
Explanation
Let H be the tower height and F its foot, with PF the horizontal distance from P. From the angle of depression β at Q, tan β = h/PF, so PF = h·cot β. From P the tower subtends angle α, so tan α = H/PF, giving H = PF·tan α = h·tan α·cot β, option C. A common error is to write h·tan α·tan β, confusing the depression angle's relation.