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CHAPTER, , 9, , Some Applications of, Trigonometry, , , , I, CASE STUDY / PASSAGE BASED QUESTIONS, , Syllabus, Trigonometric, ratios of an, acute angle of, aright-angled, triangle. Proof of, their existence, (well defined)., Values of the, trigonometric, ratios of 30°,, 45° and 60°., Relationships, between the, ratios., , -¢—__—, , Visit to Temple, , There are two temples on each bank of a river. One temple is 50 m high. A man, who is, , standing on the top of 50 m high temple, observed from the top that angle of depression, , of the top and foot of other temple are 30° and 60° respectively. (Take ¥/3 = 1.73), , , , “Ree, , D, , , , , , , , , , , , Based on the above information, answer the following questions., , (i) Measure of ZADF is equal to, (a) 45° (b) 60°, , (ii) Measure of ZACB is equal to, (a) 45° (b) 60°, (iii) Width of the river is, (a) 28.90m, (c) 25m, (iv) Height of the other temple is, (a) 325m, (c) 33.33m, , (v) Angle of depression is always, (a) reflex angle, , (c) an obtuse angle, , 30° (d) 90°, , 30° (d) 90°, , straight, , an acute angle

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o—, Observation of a Balloon, , There are two windows in a house. First window is at the height of 2 m above the ground and other window is, 4 m vertically above the lower window. Ankit and Radha are sitting inside the two windows at points G and F, respectively. At an instant, the angles of elevation of a balloon from these windows are observed to be 60° and, , , , , , , , , , , , 30° as shown belce-~, E, trie D o, tT eft, 4m FE 1, chet cm, 2m FEC) Y, L fi, A B, Based on the above information, answer the following questions., (i) Who is more closer to the balloon?, (a) Ankit (b) Radha, (c) Both are at equal distance (d) Can't be determined, (ii) Value of DF is equal to, @ 4m (b) hy¥3 m © Em (@) 2hm, v3 2, (iii) Value of h is, (a) 2 (b) 3 (c) 4 (d) 5, (iv) Height of the balloon from the ground is, (a) 4m (b) 6m (c) 8m (d) 10m, (v) Ifthe balloon is moving towards the building, then both angle of elevation will, (a) remain same (b) increases (c) decreases (d) can't be determined, , Stunt by Circus Artist, , A circus artist is climbing through a 15 m long rope which is highly stretched and, tied from the top of a vertical pole to the ground as shown below., Based on the above information, answer the following questions., , (i) Find the height of the pole, if angle made by rope to the ground level is 45°., , , , (a) 15m (b) 15J2m, 15 15, (c) B™ (d) =

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(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at, , ground level., 15, (@) sm (b) 15¥2m () 15m (d) 15V3m, (iii) Find the height of the pole if the angle made by the rope to the ground level is 30°., (a) 2.5m (b) Sm (c) 7.5m (d) 10m, (iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole., (a) 2m (b) 4m (c) 5m (d) 6m, (v) Which mathematical concept is used here?, (a) Similar Triangles (b) Pythagoras Theorem, (c) Application of Trigonometry (d) None of these, , ¢—_—, Fire Incident, , ‘There is fire incident in the house. The house door is locked so, the fireman is trying to enter the house from, the window. He places the ladder against the wall such that its top reaches the window as shown in the figure., , , , Based on the above information, answer the following questions., , (i) If window is 6 m above the ground and angle made by the foot of ladder to the ground is 30°, then length of, the ladder is, (a) 8m (b) 10m (c) 12m (d) 14m, (ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length, of the ladder is, 15, , (a) 5m (b) a m © 7m (d) 20m, , (iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find, the height of the window. (Take 3 = 1.73), (a) 4.325m (b) 5.5m (c) 6.3m (d) 2.5m, , (iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then, horizontal distance between the foot of ladder and wall is, (a) 2m (b) 4m (c) 6m (d) 8m, , (v) Ifthe fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?, (a) 5m (b) 3V5m () 3m (4) 4m

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Q—, Repairing of Electric Fault, , An electrician has to repair an electric fault on the pole of height of 8 m. He needs to reach a point 2 m below the, top of the pole to undertake the repair work., , ae, , , , 60° { _f, D c _, Based on the above information, answer the following questions., , (i) Length of BD is, , (a) 10m (b) 6m (c) 4m (d) 4m, (ii) What should be the length of ladder, so that it makes an angle of 60° with the ground?, , (a) 443 m (b) 2V3 m () 3v3_m (a) 5V3 m, (iii) The distance between the foot of ladder and pole is, , (a) 6y3 m (b) 4¥3 m () 3/3 m (4) 2¥3 m, (iv) What will be the measure of BCD when BD and CD are equal?, , (a) 30° (b) 45° (c) 60° (d) 75°, (v) Find the measure of 7DBC., , (a) 15° (b) 60° (c) 30° (d) 45°, , Application of Trigonometry for Moving Car, Rohit is standing at the top of the building observes a car at an angle of 30°, which is approaching the foot of the, , building with a uniform speed. 6 seconds later, angle of depression of car formed to be 60°, whose distance at, that instant from the building is 25 m., , , , Based on the above information, answer the following questions., , (i) Height of the building is, (a) 25V2m (b) 50m () 25/3 m (d) 25m

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(ii) Distance between two positions of the car is, (a) 40m (b) 50m (c) 60m (d) 75m, , (iii) Total time taken by the car to reach the foot of the building from starting point is, , (a) 4 sec. (b) 3 sec. (c) 6 sec. (d) 9 sec., (iv) The distance of the observer from the car when it makes an angle of 60° is, , (a) 25m (b) 45m (c) 50m (d) 75m, (v) The angle of elevation increases, , (a) when point of observation moves towards the object, , (b) when point of observation moves away from the object, , (c) when object moves away from the observer, (d) None of these, , ¢——, Light House, , A boy is standing on the top of light house. He observed that boat P and boat Q are approaching to light house, from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat, Qis 30°. He also knows that height of the light house is 100 m., , , , Based on the above information, answer the following questions., , (i) Measure of ZACD is equal to, , (a) 30° (b) 45° (c) 60° (d) 90°, (ii) If ZYAB = 30°, then ZABD is also 30°, Why?, , (a) vertically opposite angles (b) alternate interior angles, , (c) alternate exterior angles (d) corresponding angles, (iii) Length of CD is equal to, , (a) 90m (b) 60m (c) 100m (d) 80m, (iv) Length of BD is equal to, , (a) 50m (b) 100m, , (c) 100/2 m (d) 100/3 m, (v) Length of AC is equal to, , (a) 100/2 m (b) 100V3 m, , (c) 50m (d) 100m