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A tower 50 m tall stands on a plain, and a hill rises some distance away on the same level ground.
From the foot of the tower, the angle of elevation of the top of the hill is 60°; from the foot of the hill, the angle of elevation of the top of the tower is 30°.
Find the exact height of the hill (in m).

Class 10Heights and DistancesTrigonometry
  • A
  • B100
  • C150
  • D

Step-by-Step Solution

Let be the distance between the two feet. From the foot of the hill: tan m. From the foot of the tower: tan m. The value 50 m is the distance between the feet, not the height of the hill.
Answer: C) 150

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