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Some Applications of Trigonometry

Short Answer Type

91. A flagstaff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flagstaff.

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92. The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively. 30° and 45°. Find the height of the rock.

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93. From the top of a building 15 m high, the angle of elevation of the top of a tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is 45°. Find the height of the lower and the distance between the tower and the building.

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94. A boy is standing on the ground and flying .1 kite with 100m string at an elevation of 30°. Another boy is standing on the roof of a 20m high building and is flying his kite at an elevation of 30°. Both the boys are on opposite sides of both the kites. Find the length of the string such that the two kites meet.

60 m

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95. A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 45°. Calculate the distance of the cliff from the ship and the height of the cliff.

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96. A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

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97. The shadow of a vertical tower on level ground increases by 10 mts, when the altitude of the sun changes from angle of elevation 45° to 30°. Find the height of the tower.

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98. The length of the shadow of a tower standing on level plane is found to be 2x mts longer when sun's altitude is 30° than when it was 45°. Prove that the height of tower is

straight x open parentheses square root of 3 plus 1 close parentheses space mts.

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99. The angle of elevation of the top of a tower from a point on the ground is found to be 45°. By going 50 metres further away from the tower, it is found to be 30°. Find the height of the tower.

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100. The angles of depression of the top and the bottom of a 20m tall building from the top of a tower are 45° and 60° respectively. Find the height of Ihe tower.

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