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Mathematics : Some Applications of Trigonometry

Short Answer Type

111. The angles of depression of the top and bottom of an 8 m tall building from the top of a multistoryed building are 30° and 45° resp. Find the height of the multi-storyed building and the distance between the two buildings.

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112. From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks. Find the width of the river.

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113. From a point P on the ground the angles of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P.

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114. A fire at a building B is reported by a telephone to two fire-stations, F₁ and F₂ 10 km apart from each other on a straight road, F₁ and F₂ observe that the tire is at an angle of 60° and 45° respectively to the road. Which station should send its team and how much will it have to travel?

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115. The angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of the reflection of cloud in the lake is 60°. Find the height of the cloud.

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116. At the foot of a mountain the elevation of its summit is 45°, after ascending 1000 m towards the mountain up a slope of 30 inclination, the elevation is found to be 60 Find the height of the mountain.

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117. ABCDis a trapezium in which AB||CD. Line segments KS and L.M are drawn parallel to AB such that AJ = JK = KP. If AB 0.5 m and AP = BQ = 1.8 m. Find the lengths of AD, BC RS and LM.

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118. A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45°. The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds the angle of elevation of the bird from the point of observation becomes 30°. Find the speed of flying of bird.

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119. An aeroplane flying horizontally at a height of 2500 m above the ground is observed at an elevation of 60°. If after 15 seconds the angle of elevation is observed to be 30°. Find the speed of the aeroplane in km per hour.

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120. A man on a cliff observes a boat at an angle of depression of 30° which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 60°. Find the time taken by the boat to reach the shore.

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