TRIGONOMETRY - Angle Of Elevation And Angle Of Depression Based Questions.

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Frederica Stokes
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1 TRIGONOMETRY - Angle Of Elevation And Angle Of Depression Based Questions. 1. A man 1.7 m tall standing 10 m away from a tree sees the top of the tree at an angle of elevation What is the height of the tree? 2. A man sees a ship from the top of a light house 25 m high at an angle of depression of How far is the ship from the foot of the light house? 3. A rod rests against a wall. The base of the rod is 3.5 away from the wall. The angle between the rod and floor is Find the height of the wall? 4. A man standing on the top of a light house having height 200m, observe two ships approaching it at an angle of depression of 30 and 45. If one ship is just behind the other, find the distance between the ships? 5. A person standing in the bank of a river observes the top of a tree in the opposite bank, at an angle of elevation of 53. When he moved 20m backward, the angle of elevation became 27. Find the width of theriver. What is the height of the tree? 6. A boy standing at a distance of 70 m from the foot of a tower on a level surface, watches the top of the tower at an angle of elevation of Calculate the height of the tower. 7. When the sun is at an angle of elevation 48 0, the shadow of a tree is 18 m long. What is the height of the tree? CYBER MATHEMATICS

2 8. An observer found the angle of elevation of the top of the tree to be 27. After moving 10 meters closer (on the same vertical and horizontal plane as the tree), the angle of elevation becomes 54. Find the height of the tree. 9. When the sun is at an elevation of 40 0, the shadow of a tree is 10 meters. What would be the length of the shadow, when the sun is at an elevation of A balloon is in the sky at the end of a taut string 160 m long and slanted at an angle of 55 0 to the ground. How high is the balloon from the sky? 11. The height of a light house on a seashore is 800 m. If from its top, a boat is seen at angle depression of 25 0, then what is the distance of the boat from the top of the light house? 12. An object was seen at an angle depression 40 in the plain surface when observed from the top of the tower. The object is at 20m, from the bottom of the tower. Find the height of the tower. 13. The length of the shadow of a tree is 10 m less when the angle of elevation of the SUN is 60 0 than when it is 40 0, find out the height of the tree. 14. An observer standing on top of a vertical spots a house in the adjacent valley at an angle of depression of 12. The cliff is 60m tall. How far is the house from the base of the cliff? 15. A man standing on a level ground watches the top of a perpendicular tower at an angle of 65 0, After travelling 15 m CYBER MATHEMATICS Page2

3 towards the tower he watches it at If the height of the man is 1.5 m then find out the height of the tower. 16. A vertical tower stands on a horizontal place. A boy standing on the plane sees the top of a tower at an angle of elevation of By walking 25 metres towards the tower, he sees it at angle of elevation of Then, Find the height of the tower? 17. A man who is on a tree sees the top and bottom of a flag post at depression angled of 60 0 and 30 0 respectively. If the height of the flag post is 5 m, then find at which height he is sitting. 18. A boy 1.5 m tall standing on the bank of a river, sees the top of a tree on the edge of the other bank at an angle of elevation Steeping 20 m backward, he sees it at an angle of elevation of Compute the height of the tree and the width of the river. 19. A man standing at the foot of a tower 40 meters away from a hill sees the top of the hill at an angle of elevation Climbing to the top of the tower, he sees the top of the hill at an angle of elevation of Compute the height of the tower. 20. While a tower was being built, a man 1.5 m tall saw its top at an angle of elevation of The tower was completed by building up 10 m more and then the man saw its top from the same spot at an angle of elevation of What is the total height of the tower? 21. A man 1.7 m tall standing at the foot of a building 20 m high sees the top of a tree at an angle of elevation 50 0 and from the top of the Page3

4 building, he sees it at an angle of elevation of Compute the height of the tree. 22. A tower 40 m high stands in a line with two low building. From the top of the tower, these building are seen at angles of depression 50 0 and How far apart are the buildings? 23. An aircraft flying horizontally at a height of 4200 meters was seen at an angle of elevation of 31 0 at one time and after 4 seconds it was seen at 35 0 of elevation. Find the speed of the aircraft. 24. From the top of a cliff 40 m high the angle of depression and elevation of the bottom and top of a tower are observed to be 17 0 and 43 0 respectively. Find the height of the tower? 25. A man who stands 100 m away from a tower sees the top of it an elevation angle of Another man who is standing opposite to the tower sees it at an elevation angle of Find the distance between the tower and the second man. 26. A man of height 1.5m standing on top of a building of height 48.5m views another building across the square. H e observes that the angle of depression of the bottom o the building is 40 0 and the angle of depression at the top of the building is Both buildings stand on the same level ground. Calculate the distance of the man from the base of the building across the square measured along his line of sight. Calculate the height of the building 27. Rinshitha and Kavya are playing with kites. The length of the thread of both the kites are 55 m. the angle made by Rinshitha s thread with Page4

5 the ground is And that of Kavya is Whose kite is flying higher and by how much? 28. Amal and Shafeeque are flying kites from a playing ground. The length of the thread of each kite is 65 m. when the thread of the kites were fully released Amal s kite makes an angle of 45 0 and Shafeeque s kite 35 0 with the ground. Whose kite is flying high? How much? 29. When viewed from the top of a telephone tower the top of a building was seen at an angle of depression The foot of the building was seen at an angle of depression If the distance between the foot of the tower and building is 10 m, find the height of the telephone tower and building. 30. A tower is 70 m high. From the top of it, the angle of depression of the top and the bottom of a tree are found to be 45 0 and 60 0 respectively. Find the distance of the tree from the tower. What is the height of the tree? 31. A student is standing at the top of a 8 m high building views the bulb in the top of a mobile tower at an angle of elevation If the distance from the foot of the building to the foot of the mobile tower is 40 m. then find the height of the mobile tower. 32. A flagstaff is fixed on the top of building of height 20 m. a man standing on the ground observes the top and bottom of the flagstaff at the angle of 60 0 and What is the distance from the position of the man to the foot of the building? Find the length of the flag staff. Page5

6 33. A rope is tied tight from the top of a pillar to the floor. The pillar is fixed vertical from the floor. The rope makes 45 0 angle with the floor. There is 12 m from the bottom of the pillar to the floor where the rope is tied. When the rope is moved to the pillar it makes 60 0 angle with the floor. Find the distance moved by the rope towards the pillar. 34. An object was seen at an angle of depression 40 0 in the plain surface when observed from the top of the tower. The object is at 20 m, from the bottom of the tower. Find the height of the tower. (tan 40 0 =.8391) 35. A man standing on the top of a lighthouse having height 200m, observes two ships approaching it at an angle of depression of 30 0 and If one ship is just behind the other. Find the distance between the ships. 36. A boy, 1.4 m tall, standing at the edge of a river bank sees the top of a tree on the edge of the other bank at an elevation of Standing back by 3 m, he sees it at an angle of elevation of How width is the river and how tall is the tree? 37. A ladder of length 8 m is leaning against a wall. Angle made by the ladder with the floor is Find the height of the ladder above the floor on the wall. When the foot of the ladder is moved towards the wall, the angle between foot of the ladder and floor become Find the distance between foot of the ladder and the wall. Page6

7 38. A man standing on the deck of a ship, 5 m above the sea level, sees the top of a lighthouse at an angle of elevation of 70 0 and its foot at an angle of depression of How far is the lighthouse from the ship? Calculate the height of the lighthouse. 39. A man watches an object from the top of a areca nut tree, which is 20 m away from the foot of the tree at an angle of depression a. How far high is the man from the ground? b. When he climed down some distance he watches the same object at an angle of depression Draw a figure based the given details. c. If the angle of depression is 38 0, how far will he from the ground? ( tan 38 =.78) 40. From the top of an upright electric-pole on a level ground, a wire is stretched to the ground, making an angle 30 0 with the ground. The lower end of the wire is 12 meters away from the foot of the pole. Calculate the height of the pole. 41. Two perpendicular buildings on a level ground are 40 m apart. From the top of the small building the top of the big building is seen at an angle of elevation of 25 0 and the foot of the big building at an angle of depression of Find out the heights of the two buildings. 42. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60 and angle of depression of the base of the hill as 30. Find the distance of the hill from the ship and height of the hill. Page7

8 43. The angle of elevation of the top of a tower from a point A on the ground is 30. On moving a distance of 20 meters towards the foot of the tower to a point B, the angle of elevation increases to 60. Find the height of the tower and distance of the tower from the point. 44. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 and the angle of depression of the point A from the top of the tower is 45. Find the height of the tower. 45. A person standing on the bank of a river observes that the angle of the elevation of the top of a tree standing on the opposite bank is 60. When he moves 40 m away from the bank, he finds the angle of elevation to be 30. Find the height of the tree and the width of the river. 46. A statue 1.46 m tall stand 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. 47. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30 and 60 respectively. Find the distance between the two planes at that instant. 48. A tower mounted vertically on a level ground. Two children are standing on either side of the tower and are seeing the top of the Praveen Alathiyur Page8

9 tower at angle of elevation 40 0 and Children, and tower are in same line. Distance between children is 30m. Find the height of the tower. 49. The angle of elevation of the top of a building from the foot of a 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. 50. A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60 and the angle of depression of the base of the cliff is 30. Find the distance of the cliff from the ship and the height of the cliff. 51. From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30 and 45 respectively. Find the distance between the cars. 52. A ladder of length 6 m makes an angle of 45 with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60 with the floor. Find the distance between these two walls of the room. 53. The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30. If the height of the second pole is 24 m, find the height of the first pole. pg:9

10 54. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60. At a point Y, 40 m vertically above X, the angle of elevation is 45. Find the height of the tower PQ and the distance XQ. 55. 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 30 to 45 how soon after this, will the car reach the tower? 56. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30. A girl standing on the roof of 20 m high building, finds the angle of elevation of the same bird to be 45. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. 57. The angle of elevation of a jet fighter from a point A on the ground is 60. After a flight of 15 seconds, the angle of elevation changes to 30. If the jet is flying at a speed of 720 km/ hr, find the constant height. 58. The angle of elevation of an aeroplane from a point A on the ground is 60. After a flight of 30 seconds, the angle of elevation changes to 30. If the plane is flying at a constant height of , find the speed in km / hr of the plane. 59. A straight highway leads to the foot of the tower. A man standing at the top of the tower observes a car at angle of depression of 30, which is approaching the foot of the tower with a uniform speed, 6 Page10

11 second 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. 60. A pole of height 5 m is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60 and the angle of depression of the point A from the top of the tower is 45. Find the height of the tower. 61. From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 30 and 60 respectively. Find (i) The horizontal distance between the building and the lamp post. (ii) The height of the lamp post. 62. 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 that instants is 60. After some time the angle of elevation reduces to 30. Find the distance travelled by the balloon during the internal. 63. A tower stand vertically on a bank of a canal 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 20 m away from this 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 height of the tower and the width of the canal. Page11

12 64. The angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of the reflection of the cloud in the lake is 60. Find the height of the cloud from the surface of the lake. 65. The angle of elevation of the top of a vertical tower from a point on the ground is 60. From another point 10 m vertically above the first, its angle of elevation is 30. Find the height of the tower. 66. The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30 and 60 respectively. Find (i) the difference between the heights of the light-house and the building. (ii) the distance between the light-house and the building. 67. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 30. Determine the height of the tower. 68. The angles of elevations from two positions on the ground to the top of a building are complementary. The first and second positions are 'a' metre and 'b' metre away from the building. Drawing a suitable figure and show that the height of the building is abmetre. 69. A boy standing at the edge of a canal sees the top at an elevation of x 0, stepping d meters back he sees it at an elevation of y 0. How wide is the canal and how tall is the tree? Page12

13 70. From the top of a tower, an object on the ground is viewed at an angle of depression of 150. If the object is 40cm away from the foot of the tower. Calculate the height of the tower. Page13

Some Applications of trigonometry

Some Applications of trigonometry 1. A flag of 3m fixed on the top of a building. The angle of elevation of the top of the flag observed from a point on the ground is 60º and the angle of depression of