Heights and Distances Questions and Answers
Understanding Heights and Distances questions with answers is essential for anyone preparing for competitive exams like TCS, Infosys, Wipro, and Accenture placement tests. These problems are a vital part of Quantitative Aptitude, testing your grasp of trigonometry concepts such as angles of elevation and depression. Typically, these aptitude questions involve applying sine, cosine, and tangent ratios to real-life scenarios — like calculating the height of a tower, the distance of an object from a point, or the angle between two objects.
Practicing heights and distances aptitude questions with explanations helps you strengthen your problem-solving accuracy and speed — both crucial for clearing sectional cut-offs in aptitude rounds. You can practice aptitude test questions online or download PDF sets with solutions to revise systematically. Whether for campus placements or exams like AMCAT, eLitmus, or CoCubes, mastering this topic boosts your confidence and quantitative reasoning efficiency.
Solve problems based on heights and distances. Also use trigonometry basics and mensuration
Heights and Distances
31. From the top of a lighthouse 100 m high, the angle of depression of two ships is 30° and 45°. Find the distance between the ships.
- A) 57.7 m
- B) 73.2 m
- C) 100(√3 - 1) m
- D) 100(√3 + 1) m
32. A man standing on a tower observes the top of a flagpole at an angle of depression of 30°. The flagpole is 10 m tall and is 40 m away from the tower's base. Find the height of the tower.
- A) 27.31 m
- B) 33.09 m
- C) 35.31 m
- D) 40 m
33. The angle of elevation of an aircraft from a point on the ground is 60°. After 10 seconds, it changes to 30°. If the plane is flying horizontally at a height of 2000 m, find its speed.
- A) 200√3 m/s
- B) 115.47 m/s
- C) 230.94 m/s
- D) 173.2 m/s
34. A flagstaff stands on top of a tower. The angles of elevation of the top and bottom of the flagstaff from a point on the ground are 45° and 30° respectively. If the point is 20 m away from the tower's base, find the height of the flagstaff.
- A) 8.64 m
- B) 11.55 m
- C) 12.36 m
- D) 10 m
35. From a point 40 m from the base of a tower, its top is observed at 45° elevation. If the observer rises 10 m upward, the angle becomes 60°. Find the height of the tower.
- A) 35 m
- B) 46.18 m
- C) 40 m
- D) 50 m
36. From the top of a building 50 m high, the angle of depression to a car is 45°. After 10 seconds, the angle becomes 30°. Find the car's speed assuming it moves in a straight line.
- A) 14.4 m/s
- B) 12.1 m/s
- C) 10.5 m/s
- D) 8.3 m/s
37. The angles of elevation of the top of a tower from two points 100 m apart on level ground are 30° and 60°. Find the height of the tower.
- A) 86.6 m
- B) 100 m
- C) 50√3 m
- D) 75 m
38. The top of a tower is observed from a point on a horizontal plane at an angle θ. If the observer moves 10 m closer, the elevation becomes complementary to the previous. Find height of the tower in terms of θ.
- A) 10 sin2θ
- B) 10 cos2θ
- C) 10 tanθ
- D) 10/(tanθ + tan(90° - θ))
39. The shadow of a building increases by 10 m when the sun's elevation changes from 60° to 45°. Find the height of the building.
- A) 8.66 m
- B) 12.32 m
- C) 17.32 m
- D) 10 m
40. The angle of elevation of the top of a tower at a distance of x m is tan⁻¹(3/4). Find the height of the tower.
- A) 4x/3
- B) 3x/4
- C) x
- D) 5x/4