Heights and Distances Questions and Answers

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Q1
The angle of elevation of the top of a tower from a point on the ground is 30°. If the point is 20 m from the base, find the height of the tower.
  • A 10 m
  • B 20√3 m
  • C 20/√3 m
  • D 10√3 m
Answer: Option C
Explanation: Using tan 30° = height / distance, height = 20 × (1/√3) = 20/√3 m
Q2
A man standing on the ground finds the angle of elevation of a balloon to be 45°. If the balloon is 40 m above the ground, find its horizontal distance from the man.
  • A 20 m
  • B 40 m
  • C 80 m
  • D 60 m
Answer: Option B
Explanation: tan 45° = height / distance ⇒ 1 = 40/distance ⇒ distance = 40 m
Q3
From the top of a 50 m high building, the angle of depression of a car on the ground is 30°. Find the distance of the car from the base of the building.
  • A 50√3 m
  • B 50/√3 m
  • C 25√3 m
  • D 25 m
Answer: Option A
Explanation: tan 30° = height / distance ⇒ 1/√3 = 50/distance ⇒ distance = 50√3 m
Q4
The height of a tower is 30 m. A man standing at some distance finds its angle of elevation to be 60°. Find the distance of the man from the tower.
  • A 15 m
  • B 10√3 m
  • C 30/√3 m
  • D 10 m
Answer: Option C
Explanation: tan 60° = height / distance ⇒ √3 = 30/distance ⇒ distance = 30/√3 m
Q5
From a point 60 m away from the base of a tower, the angle of elevation of the top is 45°. Find the height of the tower.
  • A 60 m
  • B 30 m
  • C 60√3 m
  • D 45 m
Answer: Option A
Explanation: tan 45° = height / distance ⇒ 1 = height/60 ⇒ height = 60 m
Q6
The angle of depression of a boat from the top of a cliff 120 m high is 30°. Find the distance of the boat from the base of the cliff.
  • A 120 m
  • B 120√3 m
  • C 120/√3 m
  • D 60√3 m
Answer: Option B
Explanation: tan 30° = height / distance ⇒ 1/√3 = 120/distance ⇒ distance = 120√3 m
Q7
A tower casts a shadow 20 m long when the angle of elevation of the sun is 45°. Find the height of the tower.
  • A 10 m
  • B 15 m
  • C 20 m
  • D 25 m
Answer: Option C
Explanation: tan 45° = height / shadow length ⇒ 1 = height/20 ⇒ height = 20 m
Q8
A person observes the top of a tower at an angle of elevation of 30°. When he walks 40 m closer, the angle becomes 60°. Find the height of the tower.
  • A 20√3 m
  • B 30 m
  • C 40 m
  • D 20 m
Answer: Option B
Explanation: Let initial distance be x. Then tan 30° = h/x and tan 60° = h/(x-40). Solving gives h = 30 m
Q9
The angle of elevation of a cloud from a point 200 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud above the lake.
  • A 400 m
  • B 600 m
  • C 800 m
  • D 1000 m
Answer: Option C
Explanation: Let height = h. Using tan relations: tan 30° = (h-200)/d and tan 60° = (h+200)/d. Solving gives h = 800 m
Q10
A flagstaff stands on a 20 m high building. The angle of elevation of the top and bottom of the flagstaff are 45° and 30° respectively. Find the height of the flagstaff.
  • A 16.32 m
  • B 14.64 m
  • C 10 m
  • D 12 m
Answer: Option B
Explanation: Let flagstaff height = h. Total height = 20 + h. Using tan 30° = 20/d and tan 45° = (20+h)/d, solving gives h ≈ 14.64 m

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