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Quantitative Aptitude Practice Test: Heights and Distances
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Heights and Distances problems on: Applications of right triangles in geometry, including problems involving height and distance, angle of elevation, angle of depression, and multiple observers. Trigonometric ratios can be used to find heights and distances.  Here are some formulas related to height and distance:  Height: height=tan(angle) x  distance Distance: $B (distance)= A (height)tan (e )    Some other useful heights & distance formulas are:  sin = height/ hypotenuse  cosec = hypotenuse/ height  cos = distance/ hypotenuse  sec = hypotenuse/ distance  cot = distance/... Show more
Quantitative Aptitude Practice Test: Heights and Distances
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25 Questions

1. The angle of depression of two ships from the top of a light house are 45 and 30 degree, sailing in the same direction. If the height of the light house is 150 m, then what will be the distance between the 2 ships?
2. A kite is flying at a vertical height of 300 m making an angle of depression of 60 degree. What will be the length of thread required in this case?
3. Which of the following options is correct when angle of elevation and angle of depression are measured between two parallel planes?
4. If the value of sin X = \(\frac {1}{2}\), then what will be the of cot X?
5. If the shadow of a tower is √3 times the height of the tower, then what is the sun’s altitude at this time in degree?
6. A straight tree is broken due to thunder storm. The broken part is bent in such a way that the peak touches the ground at an angle elevation of 53°. The peak of the tree touches the ground at a distance of 15 m. What will be the height of the tree?
7. If triangle XYZ is right angled at Y, then the value of cos (X + Z) will be?
8. A bus took 60 seconds to drive down a slopy hill of height 600 m. If the angle of depression of the path is 30 degree, then what was the speed of the bus?
9. What will be the value of (sin 60 + cos 60) – (sin 30 + cos 30)?
10. If the angle of elevation of the top of a tower is 60 degree from a distance of 50 m from the base of the tower, then what will be the height of the tower?
11. An observer 1.5 m tall is 23.5 m away from a tower 25 m high. What is the angle of elevation of the top of the tower from the eye of the observer?
12. A ball is placed 50 m away from the wall of a pool. The angle of depression of the ball from the pool platform is 37 degree, then what will be the diagonal distance he will have to swim to get the ball?
13. If X + Y = 90 and cos X = 1 / 2, then what will be the value of sin Y?
14. If the height of a tower and the distance of the point of observation from its foot, both are increased by 35%, then what will happen to the angle of elevation?
15. Which of the following options is wrong about angle of depression?
16. From a point Q on a level ground, the angle of elevation of the top tower is 53 degree. If the tower is 150 m high, then what is the base distance of point Q in m?
17. Which of the following is the correct option representing tan2A?
18. If the height of a tower and the distance of the point of observation are both halved, then what will happen to the angle of depression?
19. From the top of a pole, the angles of depression of two objects P and Q situated on the same side are 30 degree and 45 degree separated by a distance of 100 m. What will be the height of this pole?
20. At some time of the day, the length of the shadow of a tower is equal to its height, then what will be the angle of elevation of the sun?
21. A 20 m ladder just reaches the top of a pole by making an angle of elevation of 30 degree. What will be the height of the pole?
22. Two fishes are swimming in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse from the two fishes is 30 degree and 45 degree. If the lighthouse is 200 m high, what is the distance between the two fishes?
23. An observer 1.5 m tall is 10√3 m away from the tower making an angle of elevation of 60 degree from his eyes. What is the height of the tower?
24. Which of the following is a correct trigonometric identity?
25. The angle of elevation of the top of a tower from a point on the ground is A. After walking a distance d towards the foot of the tower, angle of elevation is found to be B, then which of the following options is correct with respect to A and B?

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