2021 · Q49
A ladder 10 m long reaches a point 10 m below the top of a vertical flagstaff. From foot of the ladder, the elevation of top of the flagstaff is 60°. What is the height of flagstaff ?
Elementary MathematicsTrigonometry
- A12 m
- B15 m
- C16 m
- D20 m
Explanation
Let the flagstaff height be h and the ladder foot be d from its base. Then tan 60° = h/d gives d = h/√3, and the ladder (length 10) reaches height h − 10, so d² + (h−10)² = 100. Substituting d: h²/3 + (h−10)² = 100, i.e. 4h²/3 = 20h, so h = 15 m. This is option (b).