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From a point A on level ground, the top of a tower is seen at 45°. Walking 20 m up a slope inclined at 30° towards the tower, to B, the elevation of the top becomes 60°. Find the height of the tower.

Competition practiceTrigonometry
  • A10(√3 + 1) m
  • B20(√3 + 1) m
  • C10(√3 − 1) m
  • D20√3 m

Step-by-Step Solution

On the slope B is 10 m higher and 10√3 m closer. With A at distance D, h = D (45°). From B: h − 10 = √3(D − 10√3). So D − 10 = √3D − 30, D(√3 − 1) = 20, D = 10(√3 + 1) and h = 10(√3 + 1) m ≈ 27.3 m.
Answer: A) 10(√3 + 1) m

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