CBSE Class 10 Application of Trigonometry Sure Shot Questions Set A

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Study Material for Class 10 Mathematics Chapter 8 Introduction to Trigonometry

Class 10 Mathematics students should refer to the following Pdf for Chapter 8 Introduction to Trigonometry in Class 10. These notes and test paper with questions and answers for Class 10 Mathematics will be very useful for exams and help you to score good marks

Class 10 Mathematics Chapter 8 Introduction to Trigonometry

 

CBSE Class 10 Application of Trigonometry Sure Shot Questions Set A. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 m long. Determine the height of the tower.

2. An observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. Find the angle of elevation of the top of the tower from his eye.

3. A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600. When he retreats 20m from the bank, he finds the angle to be 300. Find the height of the tree and the breadth of the river.

4. A boy is standing on ground and flying a kite with 150m of string at an elevation of 300. Another boy is standing on the roof of a 25m high building and flying a kite at an elevation of 450. Find the length of string required by the second boy so that the two kites just meet, if both the boys are on opposite side of the kites.

5. An aeroplane flying horizontally 1000m above the ground, is observed at an angle of elevation 600  from a point on the ground. After a flight of 10 seconds, the angle of elevation at the point of observation changes to 300. Find the speed of the plane in m/s.

6. An aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same point on the ground are 600 and 450 respectively. Find the vertical distance between the aeroplanes at that instant. 

7. An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 450 and 600. Find the width of the river.
 
8. The shadow of a flag staff is three times as long as the shadow of the flag staff when the sun rays meet the ground at an angle of 600.Find the angle between the sun rays and the ground at the time of longer shadow.
 
9. A vertically straight tree, 15m high is broken by the wind in such a way that it top just touches the ground and makes an angle of 600
 with the ground, at what height from the ground did the tree break?
 
10. A man in a boat rowing away from lighthouse 100 m high takes 2 minutes to changes the angle of elevation of the top of lighthouse from 600 to 450 . Find the speed of the boat.
 
11. As observed from the top of a light house, 100m above sea level, the angle of depression of ship, sailing directly towards it, changes from 300  to 450. Determine the distance travelled by the ship during the period of observation.
 
12. A man standing on the deck of ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 600 and the angle of depression of the base of the hill as 300. Calculate the distance of the hill from the ship and the height of the hill. 
 
13. The angles of elevation of the top of a tower from two points at a distance of ‘a’ m and ‘b’ m from the base of the tower and in the same straight line with it are complementary, then prove that the height of the tower is √ab.
 
14. A tower stands vertically on the ground. 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°. Find the height of the tower.
 
15. An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3m 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 horizontal, 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? (You may take √3 = 1.73)
 
16. An observer 1.5 m tall is 28.5 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?
 
17. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (You may take √3 = 1.73)
 
18. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.
 
19. The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
 
20. From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
 
21. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
 
22. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
 
23. A statue, 1.6 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.
 
24. 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 50 m high, find the height of the building.
 
25. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
 
26. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

27. A man on cliff observes a boat an angle of depression of 300 which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 600. Find the time taken by the boat to reach the shore.

28. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

29. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

30. A tree is broken by the storm. The top of the tree touches the ground making an angle 30° and at a distance of 30 m from the root. Find the height of the tree.

31. A tree 12m high, is broken by the storm. The top of the tree touches the ground making an angle 60°. At what height from the bottom the tree is broken by the storm.

32. At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12 . In walking 192 m towards the tower, the tangent of the angle of elevation is 3/4. Find the height of the tower.

33. The pilot of an aircraft flying horizontally at a speed of 1200km/hr, observes that the angle of depression of a point on the ground changes from 300 to 450 in 15 seconds. Find the height at which the aircraft is flying.

34. If the angle of elevation of the cloud from a point h m above a lake is A and the angle of depression of its reflection in the lake is B, prove that the height of the cloud is
h(tanB + tanA ) /(tanB - tanA ).

35. The angle of elevation of cloud from a point 120m above a lake is 300 and the angle of depression of the reflection of the cloud in the lake is 600. Find the height of the cloud.

36. The angle of elevation of cloud from a point 60m above a lake is 300 and the angle of depression of the reflection of the cloud in the lake is 600. Find the height of the cloud.

37. The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 15 seconds, the angle of elevation changes to 300. If the jet plane is flying at a constant height of 1500√3 m, find the speed of the jet plane.

38. The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 30 seconds, the angle of elevation changes to 300. If the jet plane is flying at a constant height of 3600 √3 m, find the speed of the jet plane.

39. There are two temples, one on each bank of river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top and foot of the other temple are 300 and 600 respectively. Find the width of the river and the height of other temple.
 
40. A ladder rests against a wall at an angle α to the horizontal, its foot is pulled away from the wall through a distant a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that a/b = cos α - cosβ /sinβ - sin α.

41. From a window, h meter above the ground of a house in a street , the angle of elevation and depression of the top and the foot of another house on the opposite side of the street are Θ and Φ respectively. Show that the height of the opposite house is h (1 + tanΘcotΦ).

42. From a window, 15 meters high above the ground of a house in a street , the angle of elevation and depression of the top and the foot of another house on the opposite side of the street are 300 and 450 respectively. Find the height of the opposite house.

43. Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If α and β are the elevations of the top of the tower from these stations, prove that its inclination θ to the horizontal is given bycot θ = b cot α - a cotβ /b - a .

44. The angle of elevation of a cliff from a fixed point is θ . After going up a distance of ‘k’meters towards the top of the cliff at an angle of φ , it is found that the angle of elevation is α. Show that the height of the cliff is k(cosφ sin .cot α) /cot θ - cot α

45. A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is sin β.cosec α/2

46. The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α. On advancing ‘p’ meters towards the foot of the tower the angle of elevation becomes β. Show that the height ‘h’ of the tower is given by h = p(tanαtanβ / tanβ - tanα) m. Also determine the height of the tower if p = 150o m, α = 30o and β = 60o.

47. From the top of a light- house the angle of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light-house be ‘h’ meter and the line joining the ships passes through the foot of the light house, show that the distance between the ships is h(tanα + tanβ /tan α.tanβ ) meters.

48. An electrician has to repair on electric fault on a pole of height 4m. she needs to reach a point 1.3m below the top of the pole to undertake the repair work. What should be the height of the ladder that she should use at angle of 60o to the horizontal, would enable her reach the required position? Also, how far the foot of the pole should she place the foot of the ladder.( take √3 = 1.732)

49. The angle of elevation of a jet fighter from a point A on the ground is 60o. After a flight of 1 5 sec, the angle of elevation changes to 30o. If the jet is flying at a speed of 720 km/hr, find the constant height at which the jet is flying.

50. A man on a top of a tower observes a truck at angle of depression α where tanα = 1/√5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of truck found to be β where tanβ = √5 if the truck is moving at uniform speed determine how much more time it will take to reach the base of the tower.
 
51. At the foot of a mountain the elevation of its summit is 450; after ascending 1000m towards the mountain up a slope of 300 inclination, the elevation is found to be 600. Find the height of the mountain.

52. If the angle of elevation of cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake be β, prove that the distance of the cloud from the point of observation is 2hsec α /tanβ - tan α.

53. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height ‘h’. At a point on the plane, the angles of elevation of the bottom and top of the flag staff are α and β respectively. Prove that the height of the tower is h tanα /tanβ - tan α
.
54. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 300 to 450, how soon after this, will the car reach the tower? Give your answer to the nearest second.

55. Two pillars of equal height and on either side of a road, which is 100m wide. The angles of depression of the top of the pillars are 600 and 300 at a point on the road between the pillars. Find the position of the point between the pillars and the height of the tower.

56. The angle of elevation of the top of a tower from a point A due north of the tower is α and from B due west of the tower is β. If AB = d, show that the height of the tower is
d sinα sin β √(sin2α - sin2β)
.
57. The angle of elevation of the top of a tower from a point A due south of the tower is α and from B due east of the tower is β. If AB = d, show that the height of the tower is
d √cot2α cot2β .
 
58. From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be α and β Show that the height in miles of aeroplane above the road is given by tanα tanβ / tan α + tanβ.

59. A tree standing on horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is (b-a) tanα tan β /tanα - tanβ

60. The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun’s altitude is 300 than when it was 450. Prove that the height of tower is
x(√3 +1)m .

Please click the link below to download CBSE Class 10 Application of Trigonometry Sure Shot Questions Set A.

Chapter 01 Real Numbers
CBSE Class 10 Real Numbers Important Formulas and concepts for exams
CBSE Class 10 Real Numbers Sure Shot Questions
Chapter 02 Polynomials
CBSE Class 10 Polynomials Important Formulas and concepts for exams
CBSE Class 10 Polynomials Sure Shot Questions
Chapter 03 Linear Equations
CBSE Class 10 Pair of linear equations Important Formulas and concepts for exams
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set A
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set B
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set C
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set D
Chapter 04 Quadratic Equations
CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams
CBSE Class 10 Quadratic Equations Sure Shot Questions Set A
CBSE Class 10 Quadratic Equations Sure Shot Questions Set B
CBSE Class 10 Quadratic Equations Sure Shot Questions Set C
CBSE Class 10 Quadratic Equations Sure Shot Questions Set D
CBSE Class 10 Quadratic Equations Sure Shot Questions Set E
Chapter 05 Arithmetic Progression
CBSE Class 10 Arithmetic Progression Important Formulas and concepts for exams
CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set A
CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set B
Chapter 06 Triangles
CBSE Class 10 Triangles Important Formulas and concepts for exams
CBSE Class 10 Triangles Sure Shot Questions
Chapter 07 Coordinate Geometry
CBSE Class 10 Coordinate Geometry Important Formulas and concepts for exams
CBSE Class 10 Coordinate geometry Sure Shot Questions Set A
CBSE Class 10 Coordinate geometry Sure Shot Questions Set B
CBSE Class 10 Coordinate geometry Sure Shot Questions Set C
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Application of Trigonometry Important Formulas and concepts for exams
CBSE Class 10 Application of Trigonometry Sure Shot Questions Set A
CBSE Class 10 Introduction to Trigonometry Important Formulas and concepts for exams
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set A
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set B
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set C
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set D
Chapter 10 Circles
CBSE Class 10 Circles Important Formulas and concepts for exams
CBSE Class 10 Circles Sure Shot Questions
Chapter 11 Constructions
CBSE Class 10 Constructions Important Formulas and concepts for exams
CBSE Class 10 Constructions Sure Shot Questions
Chapter 13 Surface Area and Volume
CBSE Class 10 Surface Areas and Volumes Important Formulas and concepts for exams
CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set A
Chapter 14 Statistics
CBSE Class 10 Statistics Important Formulas and concepts for exams
CBSE Class 10 Statistics Sure Shot Questions Set A
CBSE Class 10 Statistics Sure Shot Questions Set B
CBSE Class 10 Statistics Sure Shot Questions Set C
CBSE Class 10 Statistics Sure Shot Questions Set E
Chapter 15 Probability
CBSE Class 10 Probability Important Formulas and concepts for exams
CBSE Class 10 Probability Sure Shot Questions Set A
CBSE Class 10 Probability Sure Shot Questions Set B
CBSE Class 10 Probability Sure Shot Questions Set C
CBSE Class 10 Probability Sure Shot Questions Set D
CBSE Class 10 Probability Sure Shot Questions Set E
CBSE Class 10 Probability Sure Shot Questions Set F
z Case Study Class 10 Mathematics
CBSE Class 10 Areas related to circles Important Formulas and concepts for exams
CBSE Class 10 Areas related to circles Sure Shot Questions
CBSE Class 10 Mathematics Case Studies
CBSE Class 10 Statistics Sure Shot Questions Set D
z More Study Material Class 10 Mathematics
Class 10 Mathematics All Chapters Test Paper Solved
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CBSE Class 10 Mathematics Chapter 8 Introduction to Trigonometry Study Material

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