Heights and Distances Questions and Answers

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Q41
A man standing 80 m from a tower observes a person on top raising a flag. The angle changes from 30° to 45°. Find the height of the flag.
  • A A) 32.68 m
  • B B) 46.18 m
  • C C) 33.1 m
  • D D) 20 m
Answer: Option A
Explanation: Subtract previous height from new height using tan.
Q42
The top of a tower subtends a 60° angle at the top of a building 30 m high. If the distance between them is 30 m, find tower height.
  • A A) 81.96 m
  • B B) 60 m
  • C C) 51.96 m
  • D D) 75 m
Answer: Option C
Explanation: tan 60° = opposite/base.
Q43
A man on the ground finds the angle of elevation of a bird flying horizontally to be 45°. After 5 s, it changes to 30°. If the bird is flying at 100√3 m height, find its speed.
  • A A) 100 m/s
  • B B) 50√3 m/s
  • C C) 150 m/s
  • D D) 200 m/s
Answer: Option A
Explanation: Find the horizontal distance change per second.
Q44
Two buildings are 50 m apart. From the top of the smaller, the angle of elevation of the larger's top is 30°, and the angle of depression of its base is 30°. Find height difference.
  • A A) 28.87 m
  • B B) 57.74 m
  • C C) 43.3 m
  • D D) 50 m
Answer: Option C
Explanation: Combine two tan relations.
Q45
A tower stands on a slope inclined at 30° to the horizontal. From the uphill side, the angle of elevation is 45°. Find the tower's height if horizontal distance is 50√2 m.
  • A A) 50 m
  • B B) 70.7 m
  • C C) 100 m
  • D D) 80 m
Answer: Option A
Explanation: Use slope and angle relations.
Q46
From a ship at sea, the top of a lighthouse is seen at an angle of elevation 30°. On sailing 200 m closer, angle becomes 45°. Find height of lighthouse.
  • A A) 115.5 m
  • B B) 173.2 m
  • C C) 100 m
  • D D) 141.4 m
Answer: Option C
Explanation: Two tan relations with distance difference.
Q47
The angle of elevation from a point 50 m away from a tower is 30°. From a second point further 50 m away, angle is 20°. Find height of tower.
  • A A) 36.4 m
  • B B) 28.5 m
  • C C) 32.1 m
  • D D) 30.1 m
Answer: Option B
Explanation: Use tan for both and eliminate base distances.
Q48
The angle of elevation of a kite from a point on the ground is 45°. It moves 20 m higher vertically, and the angle now becomes 60°. Find its initial height.
  • A A) 17.32 m
  • B B) 20 m
  • C C) 30 m
  • D D) 34.64 m
Answer: Option D
Explanation: Apply tan for both positions.
Q49
The top of a hill makes an angle of elevation of 30° from a point A and 45° from a point B, which is 200 m closer. Find the hill's height.
  • A A) 115.4 m
  • B B) 182.8 m
  • C C) 141.4 m
  • D D) 200 m
Answer: Option C
Explanation: Create two equations using tan and solve for height.
Q50
A tree is broken by the wind. The top touches the ground 8 m from its base. The angle between the broken part and ground is 30°. Find the original height of the tree.
  • A A) 12.62 m
  • B B) 10 m
  • C C) 13.85 m
  • D D) 15.46 m
Answer: Option C
Explanation: Use sin and cos from the right triangle geometry.

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