A woman is standing on the deck of a ship, which is h (in metres) above water level. She observes the angle of elevation of the top of a tower as 60^{\circ} and the angle of depression of the base of the tower as 30^{\circ}. What is the height of the tower?
- A. 2h
- B. 3h
- C. 4h ✓
- D. 5h
Correct Answer: C. 4h
Explanation
Let distance to tower be d. From depression angle: \tan 30^{\circ} = \frac{h}{d} \implies d = h\sqrt{3}. From elevation angle, height above deck y = d \tan 60^{\circ} = h\sqrt{3} \times \sqrt{3} = 3h. Total height of tower = 3h + h = 4h.
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