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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. If sec A = 2 / √3, then what will be the value of cos A?
2. What will be the value of tan 60 / cot 60?
3. If the height of a tower and the distance of the point of observation are both doubled, then what will happen to the angle of depression?
4. 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?
5. Two poles are x m apart and the height of one is double of the other. If from the mid – point between the two, an observer finds an elevation of their tops to be complementary, then what will be the height of the shorter pole?
6. 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?
7. Which of the following options is the correct relationship between a and b, if their measure add up to 90 degree?
8. 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?
9. 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?
10. If 0 < X < 90, then what will be the value of sec A?
11. 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?
12. If the height of a tower is 10 m and the angle a ladder that just touches its top makes with the base land is 45 degree, then what will be the base distance?
13. 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?
14. 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?
15. 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?
16. A person is standing at the top of a tower and looking down at an angle of depression of 60 degree at a distance of 30 m. What will be the height of this tower?
17. If the height of a pole and the length of its shadow are equal, then what will be the value of its angle of depression?
18. 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?
19. 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?
20. In which of the following cases angle of depression is formed?
21. If sin (20 + X) = cos 30, then what will be the value of X?
22. If the height of the tower and the base distance both are doubled, then what will happen to the elevation angle?
23. Which of the following options are correct?
24. A skier took 60 s to travel down a snowy slope of vertical height 200 m. If the angle of depression is 45 degree, then what will be the speed of the skier in m / s?
25. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse from the two ships is 30 degree and 60 degree. What is the relationship between the distances of the 2 ships from the light house?