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
21. From a top of a tower 100 m high, the angle of depression of the top of another tower is 30° and of the bottom is 45°. Find the height of the smaller tower.
- 42.26 m
- 56.7 m
- 50 m
- 57.74 m
22. A balloon is rising vertically at 5 m/s. An observer sees it at an elevation of 30° from a point 50√3 m away. Find the time taken for the angle to increase to 60°.
- 10 s
- 5 s
- 15 s
- 7 s
23. The angle of elevation to the top of a tower increases from 30° to 45° when moving 20 m closer. Find tower height.
- 20√3 m
- 40 m
- 17.32 m
- 30 m
24. From a point on the ground, the top of a tree is observed at 45° elevation. If the tree is 10 m tall, how far is the observer from it?
- 5 m
- 10 m
- 15 m
- 20 m
25. Two observers standing at points A and B, 100 m apart, observe the top of a tower at angles 30° and 45°, respectively. Find the height of the tower.
- 57.7 m
- 86.6 m
- 50 m
- 75 m
26. From the top of a 60 m high tower, the angle of depression of the top of a lamp post is 30° and that of its foot is 45°. Find the height of the lamp post.
- A) 34.64 m
- B) 38.92 m
- C) 42.36 m
- D) 30 m
27. The angle of elevation of a balloon from the ground is 45°. After ascending 120 m vertically, the elevation becomes 60°. Find the initial height of the balloon.
- A) 80 m
- B) 120 m
- C) 140 m
- D) 100 m
28. Two towers stand 150 m apart. The angle of elevation of the top of the first as seen from the foot of the second is 30°, and that of the top of the second from the foot of the first is 60°. Find the ratio of their heights.
- A) 1:3
- B) 1:√3
- C) √3:1
- D) 2:3
29. The top of a tower subtends angles of elevation of 30° and 45° from two points in the same line at distances 100 m apart. Find the height of the tower.
- A) 100 m
- B) 73.2 m
- C) 50 m
- D) 60 m
30. The angle of elevation of the top of a hill from a point on the ground is 45°. After walking 200 m toward the hill, the angle becomes 60°. Find the height of the hill.
- A) 346.4 m
- B) 273.2 m
- C) 200 m
- D) 400 m