some applications of trigonomentry

Question 1

1. If the length of the shadow of a tree is decreasing then the angle of elevation is:
   (a) Increasing
   (b) Decreasing
   (c) Remains the same
   (d) None of the above

Answer 1

(a)Increasing

Question 2

The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

(a) 10 m
(b) 30/√3 m
(c) √3/10 m
(d) 30 m

Answer 2

(b)30/√3 m
Say x is the height of the building.
a is a point 30 m away from the foot of the building.
Here, height is the perpendicular and distance between point a and foot of building is the base.
The angle of elevation formed is 30.
Hence, tan 30 = perpendicular/base = x/30
1/√3 = x/30
x=30/√3

Question 3

3. If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:
   (a) Increases
   (b) Decreases
   (c) Do not change
   (d) None of the above

Answer 3

(c)Do not change
We know, for an angle of elevation θ,
Tan θ = Height of building/Distance from the point
If we increase both the value of the angle of elevation remains unchanged.

Question 4

If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:

(a) 60°
(b) 45°
(c) 30°
(d) 90°

Answer 4

(a)60°
Hence,
tan θ = 6/2√3
tan θ = √3
tan θ = tan60°
θ = 60°

Question 5

5. The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

(a) 10√3 m
(b) 15√3 m
(c) 12√3 m
(d) 36 m

Answer 5

(a)10√3 m
Hence,
tan60° = 30/x
√3 = 30/x
x = 30/√3
x = 10√3m

Question 6

6. The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called:

(a) Angle of elevation
(b) Angle of depression
(c) No such angle is formed
(d) None of the above

Answer 6

(b)Angle of depression

Question 7

7. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:
   (a) Angle of elevation
   (b) Angle of depression
   (c) No such angle is formed
   (d) None of the above

Answer 7

(a)Angle of elevation

Question 8

8. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower standing straight is:

(a) 15√3
(b) 10√3
(c) 12√3
(d) 20√3

Answer 8

(a)15√3
We know:
Tan (angle of elevation) = height of tower/its distance from the point
Tan 60 = h/15
√3 = h/15
h=15√3

Question 9

9. The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be
   (a) Angle of elevation
   (b) Angle of depression
   (c) Line of sight
   (d) None of the above

Answer 9

(c)Line of sight

Question 10

10. The height or length of an object or the distance between two distant objects can be determined with the help of:
    (a) Trigonometry angles
    (b) Trigonometry ratios
    (c) Trigonometry identities
    (d) None of the above

Answer 10

(b)Trigonometry ratios

Question 11

11)A Technician has to repair a light on a pole of height 10 m. She needs to reach a point 1 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60∘ to the ground, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder?

Answer 11

6√3 m

Question 12

12)A statue, 2 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal

Answer 12

(B)2(√3 -1)

Question 13

13) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
a) 30m
b) 40m
c) 20m
d) 10m

Answer 13

c)20m

Question 14

14) A TV tower stands vertically on a bank of a canal, with a height of 10 √3 m . From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the distance between the opposite bank of the canal and the point with 30° angle of elevation.
a) 30m
b) 20m
c) 45m
d) 35m

Answer 14

b)20m

Question 15

15.As observed from the top of a 150 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Answer 15

(B) 150 (√3 – 1)

Question 16

16. An observer √3m tall is 3 m away from the pole 2√3 high. What is the angle of elevation of the top?
    a) 60°
    b) 30°
    c) 45°
    d) 90°

Answer 16

b)30°

Question 17

17. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. Find the height of the tower.
    a) 10+√3
    b) 10-√3
    c) 10√3
    d) 10/√3

Answer 17

c)10√3

Question 18

18. An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. What is the height of the tower?
    a) 20m
    b) 10m
    c) 40m
    d) 30m

Answer 18

d)30m

Question 19

An electrician has to repair an electric fault on a pole of height 4 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which when inclined at an angle of 60° to the horizontal would enable him to reach the required position?

a) 9√3/5
b) 9*5/√3
c) 9/√3
d) √3/5

Answer 19

A) (9√3) / 5

Question 20

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°.

a) 10m
b) 15m
c) 20m
d) 35m

Answer 20

A) 10m

Question 21

An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?

a) 40m
b) 50m
c) 45m
d) 35m

Answer 21

c)45m

Question 22

A tower stands vertically on the ground. From a point on the ground, which is 30 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 30°. Find the height of the tower.

a) 10m
b) 10√3m
c) 30√3m.
d) 30m

Answer 22

b)10√3m

Question 23

23. The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building.
    a) 5m
    b) 5(√3+3)m
    c) 15m
    d) 10m

Answer 23

b)5(√3+3)m

Question 24

24. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30° to the ground. What should be the length of the slide?
    a) 4
    b) 2
    c) 1.5
    d) 3

Answer 24

a)4

Question 25

25. A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
    a) 20√3m
    b) 30m
    c) 30√3m
    d) 60m.

Answer 25

a)20√3m

Question 26

27.The value of tan A +sin A=M and tan A – sin A=N.
The value of (M2−N2) / (MN) 0.5

a) 4
b) 3
c) 2
d) 1

Answer 26

a)4

Question 27

28. Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30°. From the top of tower B, the angle of depression of the foot of tower A is found to be 60°. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m
    a) h/2 m
    b) h/3 m
    c) √3h m
    d) h/√3 m

Answer 27

(B) h/3 m

Question 28

29. A 1.5 m tall boy is standing at some distance from a 31.5 m tall building. If he walks ’d’ m towards the building the angle of elevation of the top of the building changes from 30° to 60° . Find the length d. (Take √3 = 1.73)
    a) 30.15 m
    b) 38.33m
    c) 22.91m
    d) 34.55m

Answer 28

d)34.55m

Question 29

30. The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be 45° and 30°. Find the distance between the two objects. (Take √3 = 1.73,)
    a) 200m
    b) 150m
    c) 107.5m
    d) 73.2m

Answer 29

d)73.2m