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PARTT, , T. A, , [NCERT Exemplar), , Multiple Choice Questions, 1. The angle of elevation of the Sun when the shadow, , (e) 45, , (d)60, , 2. If a pole 6 m high casts a shadow 2/3 m long on the, ground, then the Suns elevation is, (a) 60°, , (b) 45, , (c) 30°, , (d) 90°, , (b) 16 m, , (c) 18 m, , (d) 19 m, , 8. A ramp for disabled people in a hospital have slope, of the ramp be 1m, then the, 30°. If the, , length, , of ramp is, , (a) 2 m, , b) 0.5 m, , (c) 2/3 m, , (d) I m, , 9. A kite is, , flying at a height of 80 m, , ground. The string attached to, , 3. If 300/3 m high tower makes an angle of elevation, at a point on ground which is 300 m away from its, , foot, then the angle of elevation is, , distance of the point from the foot of tower is, , 10. The, , length, , height of kite is, , D, , (b 45, , 8, (c) 60°, , (d) 90°, , 6. 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, then the height of pole,, if the angle made by the rope with the ground level, is 30°, is, (a) 5 m, , (c)15m, , point, , on, , (b) 78.05 m, , (d) None of these, , 11. A tower stands near an airport. The angle of, , elevation 0 of the tower from a point on the ground, is such that its tangent is 5/12. The height of the, tower, if the distance of the observer from the tower, is 120 m is, [CBSE 2015], (b) 50 m, (a) 40 m, (c) 60 m, (d) 70 m, , 4 M, , a) 30°, , a, , 8, , (a) 75 m, (c) 226 m, , [CBSE 2013], , kite and, , with the ground level such that tan6 =then the, , (cd) 30/3 m, , oint A. The angle of depression from A is, , a, , the ground is 85 m. If the string makes an angle 6, 5, , (a) 180 m, , 4V3m, , a, , of a string between, , (c) 150 m, , 5. The figure shows the observation of point C from, , the kite is, , b) 92.37 m, (d) 72.57 m, , (b) 60/3 m, , c, , to, , (e) 52.57 m, , (d) 60°, (c)45, 4. From the top of a 60 m high tower, the angle of, depression of a point on the ground is 30°. The, , above the, , point on the ground. The, inclination of the string with ground is 60°, then the, length of the string is, , temporarily tied, , (a) 62.37 m, , (b) 30, , (a) 0°, , (a) 10 m, , height, , of a pole h m high is v3 h m long is, b) 30°, , of the, , with the horizontal. If the foot, 60, 9.5 m away from the wall. The length of the ladder is, , objective Questions, (a) 0°, , angle ot, leaning against a wall, makes anladder, is, , ladder,, , 12. The top of two poles of height 20 m and, 14 m are connected by a wire. If the wire makes an, angle of 30° with the horizontal, then the length of, the wire is, (a) 12 m, , (b) 10 m, , (c) 8 m, , (d) 6 m, , 13. An observer, 1.5 m tall is 20.5 m away from a tower, , 22 m high, then the angle of elevation of the top of, (b) 10 m, , the tower from the eye of the observer is, , (d) 20 m, , (a) 30, , (b)45°, , (e) 60, , (d) 90°

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96, , MathematicsX (Standard), , CBSE Term Il, , 14. The, , angle of elevation of the top of the, , tower from, , a, , Value of DF is, , (ii), , point, which is 40 m away from the base of the, tower in the horizontal level, is 45°. Find the height, of the tower., (a) 70 m, , (a)m b)hV3, , 15. The, , angle of elevation of the top of a building, 150 m high, from a, point on the ground is 45°. The, , to, , m, , m, , d)m, , Value of h is, , (ii), , (b) 60 m, (d) 30 m, , (c) 40 m, , equal, , (a) 2, , (b) 3(3+ 1), , (c) 4, , d)3-1), , (iv) Height of the Parachute from the ground is, , distance of the point from foot of the building is, , (a) 4 m, , (b) 3(4-3), , (a) 120 m, , c) 8 m, , (d) 3(4+3), , (b) 130 m, (d) 150 m, , (c) 140 m, , 16. The, , angle, , of depression of the, , car, , parked on, , the, , road from the top of a 150 m high tower is 30°. The, , distance of the car from the tower is, (a) 150 m ( b ) 75 m, 17. From, , a, , point, , on, , the, , (c) 150/3 m, , ground,, , the, , angles, , [CBSE 2014], 0, , (d)m, V3, , of elevation, , (v) If the Parachute is moving towards the building, then both angles of elevation will, (a) remain same, (b) increases, (d) Can't be determined, () decreases, 20. A cyclist is climbing through a 20 m long rope, which is highly stretched and tied from the top of a, vertical pole to the ground as shown below, , 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, then the height of the tower is, (a) 14.64 m, (c) 38.64 m, , (b) 28.64 m, (d) 19.64 m, , 18. A bridge on a river makes an angle of 45 with its, , edge. If the length along the bridge from one edge, to the other is 150 m, then the width of the river is, (a) 107.75 m, (c) 75 m, , (b) 105 m, (d) 106.05 m, , Based on the above information, answer the, , following questions., (i) The height of the pole, if angle made by rope with, the ground level is 60°, is, , Case Based MCQas, , (a) 15 m, , 19. There are two balcony in a house. First balcony is, at a height of 3 m above the ground and other, balcony is 6 m vertically above the lower balcony., Ankit and Radha are sitting inside the two balcony, at points C and E respectively. At any instant, the, angles of elevation of a Parachute from these, balcony are observed to be 60° and 45° as shown, below, , 35, , hm, , c)20, , 3, , 3 m, , AL, , Based on the above information, answer the, , following questions., (i) Who is more closer to the Parachute., (a) Ankit, , (b) Radha, (c) Both are at equal distance, (d) Can't be determined, , 15, , (d), , m, , V2, , (i) If the angle made by the rope with the ground, level is 60°, then the distance between artist and, pole at ground level is, 10, , (a) V2, , (b) 10/2 m, , (c) 10 m, , (d) 10/3 m, , (iii) If the angle made by the rope with the ground, level is 45°. The height of the pole is, (a) 2.5 m, (c) 7.5 m, , 6m, , G60, , (b) 10/3 m, , (iv), , (b) 10 m, , (d) 10/2 mn, , If the angle made by the rope with the, ground, level is 45° and 3 m rope is broken, then the height, of the pole is, , (, , 17, , (b) 7 m, , (c) 14 m, , (d) 72 m, (v) Which mathematical concept is used herer, (a) Similar triangles, , (b) Pythagoras theorem, (c) Application of trigonometry, , (d) None of the above

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97, , eaSE Term lIl | Mathematics X (Standard), , 21. A group of students of class X visited India Cate on, , aneducational trip. The teacher and students had, interest in history as well. The teacher narrated that, , India Gate, official name Delhi Memorial,, originally called All-India War Memorial,, monumental sandstone arch in New Delhi,, dedicated to the troops of British India who died in, wars fought between 1914 and 1919.The teacher, , of, distance between the peaks, respectively. If the, satellite is, , km, and the, distance, of, vertically above the mid-point the, V3, =1.73), between the two mountains. (use, , two mountains is 1937, , also said that India Gate, which is located at the, eastern end of the Rajpath (formerly called the, Kingsway), is about 138 feet (42 m) in height., , B, , (G), , Nanda devi, , Mullayanagri, , The distance of the satellite from the top of Nanda, Devi is, (a) 1139.4 km, , (c)1937km, , (b) 1119.65 km, (d) 1025.36 km, , of the satellite from the top of, Mullayanagiri is, (b) 577.52 km, (a) 1139.4 km, , ii) The distance, , (i) What is the angle of elevation if they are standing, at a distance of 42 m away from the monument?, , 30, , (b) 45, , (d) o, (c) 60, (ii) They want to see the tower at an angle of 60°. So,, they want to know the distance where they should, stand and hence find the distance., (a) 25.24 m, , (b) 20.12 m, , (c) 42 m, , (d) 24.24 m, , (ii) If the altitude of the Sun is at 60°, then the height, of the vertical tower that will cast a shadow of, length 20 m is, , (a) 20V3 m, , (, , 15, , (b), , 20, , 3, , (d) 1025.36 km, , (iii) The distance of the satellite from the ground, (a) 1139.4 km, , (c)1937 km, , is, , (b) 567.64 km, (d) 1025.36 km, , (iv) What is the angle of elevat on, if a man is standing, at a distance of 7816 m from Nanda Devi?, (a) 30°, , (b) 45, , (c) 60, , (d) o, , (v)Ifa mile stone very far away, makes 45° to the top, of Mullayanagiri mountain. Hence, find the, distance of this mile stone from the mountain., (a) 1118.327 m, (c) 1930 m, , (b) 566.976 m, (d) 1025.36 m, , m, , (d) 15/3 m, , (iv) The ratio of the length of a rod and its shadow is, , 1:1. The angle of elevation ofthe Sun is, (b) 45°, , (a) 30°, (c) 60°, , (c)1937km, , (d) 90°, , () The angle formed by the line of sight with the, horizontal when the object viewed is below the, horizontal level is, , (a) corresponding angle, (b) angle of elevation, (c) angle of depression, , (d) complete angle, 22. A Satellite flying at height h is watching the top of, the two tallest mountains in Uttarakhand and, , PART 2, Subjective Questions, Short Answer Type Questions, 1. If the height of a tower and the distance of the, point of observation from its foot, both are, increased by 10%, then the angle of elevation of its, top remains unchanged. Explain., 2. A straight tree is broken due to thunderstorm. The, broken part is bent in such a way that the peak of, the tree touches the ground at an angle of 60° ata, , distance of2/3 m. Find the whole height of the tree., 3. Determine the height of a mountain, if the, , Karnataka they being Nanda Devi (height 7,816m), , elevation of its top at an unknown distance from the, , and Mullayanagiri (height 1,930 m). The angles of, from the satellite to the top of Nanda, depression, Devi and, , base is 30° and at a distance 10 km farther off from, the mountain, along the same line, the angle of, , Mullayanagiri are 30°and 60°,, , elevation is 15°. (take tan 15° = 0.27)

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CBSE Term, , 98, 4. There is a flag staff on a tovwer of height 20 m. At a, , point, on the ground, the angles of elevation of the, foot, and top of the, , flag are 45° and G60°, respectively., , Find the height of the flag stalf., , 5. If the length of the shadow of a tower is, increasing, then the angle of elevation of the Sun is also, , Mathematics X (Standard, , 15. The angle of elevation ofanaeroplane from a point, on the ground is 45°. Alter lying for 15 s, the angla, of elevation changes to 30°. If the aeroplane is, flying at a constant height of 2500 m, then find the, CBSE 2013), average speed of the aeroplane., , 16. The shadow of a flag staffis three tines as long as the, shadow of the flag stafl, when the Sun rays meet the, , increasing. Why or why not?, 6. A window in a building is at a height of 10 m from, the ground. The angle of depression of a point P on, the ground from the window is 30°, The angle of, elevation of the top of the building from the point P, is 60°. Find the height of the building., [CBSE 2007], 7. A player sitting on the top ofa tower of height 20 mn, , observes the angle of depression of a ball lying on, the ground as 60°. Find the distance between the, , foot of the tower and the ball., 8. If two towers of height x m and y m subtend angles, , of 30° and 60°, respectively at the centre of the line, joining their feet, then find x : y., [CBSE 2015], 9. Ifa man standing on a platform 3 m above the, surface ofa lake observes a cloud and its reflection, in the lake, then the angle of elevation of the cloud, is equal to the angle of depression of its reflection., State true or false. Justify., 10. From the top of a hill, the angles of depression of, two consecutive kilometre stones due East are, found to be 30° and 45°. Find the height of the hill., [CBSE 2015], , 11. The shadow of a tower is 30 m long, when the Sun's, angle of elevation is 30°. What is the length of the, shadow, when Sun's elevation is 60°, 12. Two ships are there in the sea on either side ofa, light house in such a way that the ships and the base, of the light house are in the same straight line., The angle of depression of two ships as observed, from the top of the light house are 60° and 45°., , If the height of the light house is 200 m, then find, the distance between the two ships., CBSE 2014], 13. From the top of a tower of height 50 m, the angles, of depression of the top and bottom of a pole are 30, and 45°, respectively. Find, CBSE 2015], of, the, tower., bottom, from, is, the, the, pole, (i) how far, , (i) the height ofthe pole. [take, 3, , Il, , =1.732], , 14. A man standing on the deck of a ship, which is 10 m, above the water level. He observes that the angle of, , elevation of the top of a hill is 60 and the angle of, depression of the base of the hill is 30°. Calculate, the distance of the hill from the ship and height of, CBSE 2016], the hill., , ground at an angle of 60°. Find the angle between the, Sun rays and the ground at the time of longer shadow., , 17. 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 elevation, , of two planes from the same point on the ground, are 60 and 45°, respectively. Find the vertical, distance between the aeroplanes at that instant., , 18. There is a small island in the middle of a 100 m, wide river and a tall tree stands on the island. P and, are points directly opposite to each other on two, banks and in line with the tree. If the angles of, , elevation of the top of the tree from Pand Q are, respectively 30° and 45°, then find the height of the, tree. [take,V3 = 1.732], , Long Answer Type Questions, 19. An aeroplane is at an altitude of 1200m. If two, , ships are sailing towards it in the same direction., , The angles of depression of the ships as olbserved, from the aeroplane are 60° and 30°, respectively., , Find the distance between both ships., , 20. The angles of depression of two consecutive kilometre, stones on the road on right and left of an aeroplane, are 60 and 45°, respectively as observed from the, aeroplane. Find the height of the aeroplane., 21. The angle of elevation of the top ofa tower at a, , distance of 120 m from a point A on the ground, is 45°. If the angle of elevation of the top of a flag, staff fixed at the top of the tower, at A is 60°, then, , find the height of the flag staff. [use, V3 =1.73], [CBSE 2014, , 22. A balloon is connected to an electric pole. It is, , inclined at 60 to the horizontal by a cable of length, 215 m. Determine the height of the balloon from, the ground. Also, find the height, the angle of inclination is changed from 60° to 30°., , ofthe balloon, if, , [CBSE 2015], , 23. A man in a boat rowing away from a light house 100, m high takes 2 min to change the angle of elevation of, , the light house from 60 to 45°. Find the speed of, , boat.

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cBSE Term, , ll, , 99, , | Mathematics X (Standard), , certain point is 30. If the observer moves 20 m, , the opposite side of the lane are found to be a and B,, Prove that the height of the other house, , towards the tower, the angle of elevation of the top, , is h(1+ tan d cot B) m., , 24. The angle of elevation of the top of a tower, , increases by 15°. Find the height of the tower., 25. The shadow of a tower standing on a level plane is, , found to be 50 m longer when Sun's elevation is 30, than when it is 60". Find the height of the tower., , 26. A vertical tower stands on a horizontal plane and is, surmounted by a vertical flag staff of height h. Ata, , point on the plane, the angles of elevation of the, bottom and the top of the flag staff are a and B, respectively. Prove that the height of the tower is, , respectively., , 32. The lower window of a house is at a height of 2 m, above the ground and its upper window is 4 mn, vertically above the lower window. At any instant the, angles of elevation of a balloon from these windows, are observed to be 60° and 30°, respectively. Find, , the height of the balloon above the ground., , Case Based Questions, 33. A girl 8 m tall spots a parrot sitting on, , the top ot a, The angle, the, from, ground., building, of elevation of the parrot from the eyes of girl at, any instant is 60°. The parrot flies away, of height 58, , h h tana, , tan -tan a., 27. The angle of elevation of the top of a tower 30 m, high from the foot of another tower in the same, plane is 60° and the angle of elevation of the top of, the second tower from the foot of the first tower is, 30°. Find the distance between the two towers and, also the height of the tower., , m, , way that it remained at a, constant height from the ground. After 8 s, the, angle of elevation of the parrot from the same point, is 30°., , horizontally in such a, , 28. From the top of a tower h m high, angles of, depression of two objects, which are in line with the, foot of the tower are a and B (B> x). Find the, distance between the two objects., 29. A ladder against a vertical wall at an inclination 0. to, the, horizontal. Its foot is pulled away from the wall, through a distance p, so that its upper end slides a, distance q down the wall and then the ladder makes, an angle Bwith the horizontal. Show that, , P cos-cos a, sin a, , - sin ß, , 30. 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 45°. Find the height of the tower., , 31. A window of a house is h m above the ground. From, the window, the angles of elevation and depression of, the top and the bottom of another house situated on, , 60, 30, , 8m, , Based on the above information, answer the, following questions. (Take v3 = 1.73), (i) Find the distance of first position of the parrot, from the eyes of the girl., i) If the distance between the position of parrot, increases, then the angle of elevation decreases., Justify with girl., (iii) Find the distance between the girl and the building., (iv) How much distance covers parrot covers?, (v) Find the speed of the parrot in Ss.