Chap-9 MCQs - AMU/JMI XI-Dip.Engg. Entrance Test

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Chapter 9 : Some Applications of Trigonometry          Answers
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1. The line of sight is
a)      The line drawn from the eye of an observer parallel to the ground
b)      The line drawn from the eye of an observer to the point in the object viewed by the observer.
c)      The line drawn from the eye of an observer perpendicular to the ground
d)     None

2. When an object is viewed above the horizontal line, the angle formed by the line of sight with the horizontal is known as

a)      Angle of elevation

b)      Angle of depression

c)      Elevated angle

d)     Depressed angle

3. When an object is viewed below the horizontal line, the angle formed by the line of sight with the horizontal is known as

a)      Angle of elevation

b)      Angle of depression

c)      Elevated angle

d)     Depressed angle

4. What is the angle of elevation of the top of the pole of height 5  m when viewed from a point on the ground, which is 5 m away from the foot of the pole?

a)      15°

b)      30°

c)      45°

d)      60°

5. What is the angle of elevation of the top of the pole of height 6  m when viewed from a point 1m high from the ground and 5 m away from the foot of the pole?

a)      15°

b)      30°

c)      45°

d)     60°

6. At what angle with ground should a ladder of length 2  meter be kept so that its top touches the vertical wall a height of 3 m from the ground?

a)      15°

b)      30°

c)      45°

d)     60°

7. A man of height 1.6m is standing 30m away from a building. Find the height of the building if the angle of elevation of the top of the building from his eyes is 45°.

a)      28.4m

b)      30m

c)      31.6m

d)     40.0m

8. From a point on the ground, the angle of elevation of the bottom and top of a pole on 10m high building are 45° and 60 respectively. Find the height of the pole.

a)      4.41 m

b)      5.23 m

c)      7.32 m

d)     10.5 m

9. The angle of elevations of top of a 10m high building from two different points are 45° and 30° respectively. Find the distance between the two points if the two points and bottom of the building are in same line.

a)      4.41 m

b)      5.23 m

c)      7.32 m

d)     10.5 m

10. Two building of 20m heights each are standing opposite each other on either side of the road. From a top of the buildings, the angle of depressions on a point between them on the road, are 60° and 30°. Find the width of the road.

a)      25 m

b)      27.32 m

c)      25.41 m

d)     30 m

11. An electric pole of height 7 m bends from a certain height and touches the ground at distance 5 m away from the base of the pole. Find the ht at which the pole is bent.

a)      3 m

b)      4 m

c)      7/11

d)     11/7

12.  An helicopter is flying in horizontal line at a height of 500m from the ground. The angle of elevations of the helicopter from a point on the ground, between time interval of 100 seconds were 45° and 30° degree. Find the speed of the helicopter.

a)      366 m/s

b)      3.66 m/s

c)      450 m/s

d)     4.50 m/s

13. An helicopter at a height of 1000m is seen from two different cities at the same time with an angle of elevation of 30° and 45° respectively. If the helicopter and the two cities were in the same vertical plane, find the distance between two cities.

a)      2.732 kms

b)      3.732 kms

c)      2.536 kms

d)     5.536 kms

14. A kite is flying at a height of 101 m above the ground. The lower end of the string is 1.5 m above the ground. The inclination of the string with the ground is 45°. Find the length of the string, assuming that there is no slack in the string.

a)      173.2 m

b)      141.4 m

c)      132.5 m

d)     121.5 m

15. A 1.5 m tall boy is standing at some distance from a hill. The angle of elevation from his eyes to the top of the hill increases from 30° to 45° as he walks towards the hill

Find the height of the hill.

a)      998.5 m

b)      1000.0 m

c)      1001.5 m

d)     1010.5 m

16. From a point on the ground, the angles of elevation of the bottom and the top of a flag fixed at the top of a 100 m high building are 45° and 46° respectively. Find the height of the tower. (tan46 ° = 1.0355)

a)      1.55m

b)      3.55m

c)      3.75 m

d)     4.05m

17. The angle of elevation of the top of a building A from the foot of the building B is 30° and the angle of elevation of the top of the building B from the foot of the building A is 60°. If the building A is 50 m high, find the height of the building B.

a)      100

b)      200

c)      300

d)     400

18. From the top of a 10 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

a)      27.32

b)      25.32

c)      17.5

d)     16.5

19. A man on bike with uniform speed on straight road leading to a building. A man standing on the top of the building observe the man at angle of depression of 30° and then after 10 seconds at an angle of 60°. Find the speed of the man to reach the foot of the building from the point when angle of depression was 60°.

a)      5 s

b)      10 s

c)      15 s

d)     20 s

20. The angle of elevations of a tower from two points 4m and 25m away from base of the tower and in the same straight line are complementary Find the height of the tower.

a)      5

b)      10

c)      15

d)     20

21. The angle of elevation of a point P when observed from the ground is 10°. The point P lies

a)      on the ground

b)      below the ground

c)      above the ground

d)     Anywhere in the space

22. When the shadow of the object in the sun is equal to the  height of the object, the angle of elevation of the sun is

a)      30°

b)      45°

c)      60°

d)     None

23. When the shadow of the object in the sun is equal to the height of the object, the angle of elevation of the sun is

a)      30°

b)      45°

c)      60°

d)     None

24. The ratio of an object to its shadow is    , the angle of elevation f the source of light is

a)      30°

b)      45°

c)      60°

d)     None

25. Two building are of heights 40m and 100m. Find the length of the rope required to connect the building from its tops, if the angle of depression of top of small building from the top of higher building is 60.

a)      10

b)      20

c)      30

d)     40

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