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A vertical tower 10 m high carries a flagstaff standing upright at its top. From a point on level ground the angle of elevation of the top of the tower is 30° and that of the top of the flagstaff is 45°. The length of the flagstaff is:

Competition practiceTrigonometry
  • A10(√3 − 1) m
  • B10(√3 + 1) m
  • C10√3 m
  • D20 m

Step-by-Step Solution

The ground distance is d = 10/tan30° = 10√3 m. The top of the flagstaff is d·tan45° = 10√3 m above the ground, so the flagstaff itself is 10√3 − 10 = 10(√3 − 1) ≈ 7.32 m. The value 10√3 ≈ 17.32 m is the total height of tower plus flagstaff.
Answer: A) 10(√3 − 1) m

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