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Mathematics : Some Applications of Trigonometry

Short Answer Type

101. A vertical tower stands on a horizantal plane and is surmounted by a flagstaff of height 6 m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the flagstaff is 45°. Find the height of the tower.

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102. Two men on either side of a cliff 80 m high observe the angles of elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

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103. Nimit wants to find the height of the top of a hill. He observes that the angles of elevation of the top of the hill at points C and D, 300 m apart, lying on the base of the hill and on the same side of the hill are 30° and 45° respectively. What is the height of the hill?

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Long Answer Type

104.

Tanvika standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When she is 40 m away from the bank she finds the angle of elevation to be 30°. Find
(i) the height of the tree.
(ii)the width of the river.

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Short Answer Type

105. 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 found to be 45°. Determine the height of the tower and the distance between the tower and the building.

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106. From a window (60 mts high above the ground) of a house in street the angles of elevation and depression of the top and the foot of another house on opposite side of street are 60 and 45° respectively. Show that the height of the opposite house is

60 open parentheses 1 plus square root of 3 close parentheses space mis.

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107. A tree breaks due lo the storm and the broken part bends so that the lop of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 mis. Find the height of the tree.

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108. A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance between Ihe two cars and how far is each car from the tower.

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109. A tower stands on the ground. From a point on the ground which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.

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110. An electrician has to repair an electric fault on a pole of height 4m. She needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use at an angle of 60° to the horizontal, would enable her to reach the required position ? Also, how far from the foot of the pole should she place the foot of the ladder.

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