Some Applications of trigonometry

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Gwendoline Potter
5 years ago
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1 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 that point from the top of the tower is 45º. Find the distance of flag from the point of observation. 2. From the top of a tree of 30 m height, the angle of elevation of the top and the angle of depression of the bottom of a tower standing on the same plane are observed to be 30º and 60º respectively. Find the height of the tower. 3. A ladder 12 3 m long, resting against a wall makes an angles of 60º with the ground. a) Find the distance of the ladder from the wall. b) How high on the wall does the ladder reach? 4. A boy, 1.5 m tall is 60m away from a tower of 31.5 m heigh. What is the angle of elevation of the top of the tower from his eye. 5. A hospital is in between a school, and a tower and all are on a straight line. The distance from the tower to school is 120 m and the angle of elevation of the top of the tower from the top of the hospital is 30º. From the same point, the angle of depression of the top of the school is found to be 45º and the bottom of the tower is 60º. If the height of the school is 20m, then find the heights of the hospital and the tower. 6. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30º. A girl standing on the roof of 20m high building finds the angle of elevation of the same bird to be 45º. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.

2 7. The difference in the lengths of the shadow of an electric post when the sun is at angles of elevation 30º and 60º is 6 meters. Find the height of the post. 8. From the top of a cone of base radius 21 cm and height 72 cm, a cone of slant height 25 cm is cut off. What is the volume and curved surface area of the remaining portion? 9. A man of height 1.6m saw the top of a tree at an angle of elevation 30º. After 1 year the same man saw its top, 42 cm more, from the same spot at an angle of elevation 60º. What is the total height of the tree? 10. An aero plane, when 3000 m high, passes vertically above another aero plane at an instant, when the angle of elevation of the two aero planes from the same point on the ground are 60º and 45º respectively. Find the vertical distance between the aero planes. (use 3 = 1.73) 11. A man standing on the deck of a ship, which is 10m above water level, observes the angle of elevation of the top of a hill as 60º and angle of depression of the base of the hill as 30º. Find the distance of the hill from the ship and height of the hill. 12. The bottom of a ladder makes an angle 60º with the floor when it is slanted on a wall. The distance of the ladder from the wall is 45 cm. The ladder slides a little downwards, and then the new angle is 30º and the top of the ladder moves 3 cm downwards. Find the length of the ladder. 13. A man is standing on a tree of height 2.1m, 50 m away from the foot of a tower of height 90m. Find the angle of elevation of the top of the tower if the height of the man is 1.3m 14. From a window x metres high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street are a and b respectively. Show that the height of the opposite house is x (1 + tan a cot b) metres.

3 15. An electric post height 15 ft. has a shadow of same length at a particular time. Find the angle of elevation of the sun from the end of the shadow at this time. 16. From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometer stones on the opposite sides of the aero plane tanatanb are found to be a and b. Show that the height of the aeroplane is tana+tanb 17. The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30º. On advancing 150 meters towards the foot of the tower, the angle of elevation becomes 60º. Show that the height of the tower is 129 meters. (use 3 = 1.732) 18. Peter is looking up at the top of a statue of height 11 ft. 45 feet up in a tower. Peter is 56 3 feet away from the building, across the street. Find the angle of elevation of the top of the statue. Also find the distance of the top of statue from peter. 19. The height of a house subtends a right angle at the opposite window. The angle of elevation of the window from the base of the house is 60º. If the width of the road is 6 m, find the height of the house. 20. A flag of 3m fixed on the top of a tower. The angle of elevation of the top of the flag observed from a point on the ground is 45º and the angle of depression of that point from the top of the tower is 30º. Find the distance of flag from the point of observation. 21. A man standing on the deck of a ship which is 40m 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. 22. The angle of elevation of a jet plane 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 plane is flying at a constant height of m. find the speed of the jet plane.

4 23. The angle of elevation of the top of a rock from the top and bottom of a 100m high tower is 30 is 30 and 45 respectively. Find the height of tbe rock. 24. A person standing on the bank of a river observe that the angle of elevation of the top of tree standing on the opposite bank is 60. When he moves 40m 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. 25. An aeroplane, when 3000m high, passes vertically above another aeroplane at an instance when the angles of elevation of the two aeroplanes from the same point on the ground are 60 and 45 respectively. Find the vertical distance between the two aeroplanes. 26. A pole 5m high is fixed on the top of a tower. The angle of eleavation of the top of the pole observed from a point on the ground is 60 and the angle of depression of the same point from the top of the tower is 45. Find the height of the tower. 27. From the top of a tower, the angles of depression o f two objects on the same side of the tower are found to be a and b (a>b). If the distance between the objects is p metres, show that the height h of the tower is given by : h = ptanatanb (tana tanb) 28. The angle of elevation of a jet plane from a point P on the ground is 60. After a flight of 15 seconds, the angle of elevation changes to 30. If the jet plane is flying at a constant height of 1500 m. find the speed of the jet plane in km/h 29. The angle of elevation of a cloud from a point 60 meters above a lake is 30 and the angle of depression of its reflection in the lake 60. Find the height of the cloud. 30. The angle of elevation of the top of a rock from the top and bottom of a 100m high tower is 30 and 45 respectively. Find the height of the rock.

5 31. A person standing on bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60. When he moves 40m 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. 32. An aeroplane, when 3000m high, passes vertically above another areoplane at an instance when the angles of elevation of the two aeroplanes from the same point on the ground are 60 and 45 respectively. Find the vertical distance between the two aeroplanes. 33. A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60 and the angle of depression of the same point from the top of the tower is 45. Find the height of the tower. 34. The angle of elevation of the top tower as seen from two points A and B situated in the same line and at a distance p and q respectively from the foot of the tower, are complementary, Prove taht the height of the tower is pq. 35. Two poles of equal heights are standing opposite to each other on either side of a road., which is 100 metre wide. From a point between them on the road, the angles of elevation of their tops are 30 and 60. Find the position of the point and also the heights of the poles. 36. A man standing on top of a multi-storeyed building 45m high is looking at two advertising pillars on the same side whose angles of depression are 30 and 60 respectively. What is the distance between the pillars? (Assume the two pillars as two points on the level ground and in the same straight line)

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

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 50 0. What is the height