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Mathematics : Some Applications of Trigonometry

Short Answer Type

151. 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 the cloud in the lake is 60°. Find the height of the cloud.

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152. As observed from the top of a 75 m high lighthouse (from sea-level), the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light-house, find the distance between the two ships.

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153. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. If the plane is flying at a constant height of

3600 square root of 3 comma space end root

find the speed in km/hr, of the plane.

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154.

An aeroplane, when 3000 m high passes vertically above another aeroplane at constant, when the angle of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between aeroplanes.

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155. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at angle of depression of 30°, which is approaching the foot of the tower with a uniform speed 6 seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from the point.

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156. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.

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157.

From the top of a building 60 m high, the angles of depression of the lop and bottom of a vertical lamp post are observed to be 30° and 60° respectively. Find
(i) the horizontal distance between the building and the lamp post.
(ii) the height of Ihe lamp post.

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158. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon Irom the eyes of the girl at that instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

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159.

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of Ihe tower from this point.

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160. The angles of depression of the top and bottom of an 8 m tall building from the top of a multistroyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

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