2023 · Q55
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° and the angle of depression of the base of the tower as 30°. What is the height of the tower?
Elementary MathematicsTrigonometry
- A2h
- B3h
- C4h
- D5h
Explanation
Let the horizontal distance to the tower be d. From the woman's eye level, tan30° = h/d gives d = h√3 for the base below her. For the top, tan60° = (H − h)/d gives H − h = d√3 = 3h. Hence the tower's height is H = 4h (C).