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Some Applications of Trigonometry

Short Answer Type

131. 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 60°. Find the height of the tower and the distance between the tower and the building.

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132. The angle fo elevation of an aeroplane from a point P on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of

open parentheses bold 1 bold plus square root of bold 3 close parentheses

find the speed of the aeroplane.

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133. 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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134.

From the top of a tower 100 m. high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 30° and 45° respectively. Find the height of the pole.

From a point P on the ground, the angles of elevation of the top of a 10 m. tall building and a helicopter, hovering at some height over the top of the building are 30° and 60° respectively. Find the height of the helicopters above the ground.

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135.

The angles of elevation and depression of tine top and bottom of a lighthouse from the top of a building 60 m, are 30° and 60° respectively. Find :
(i) The difference between the heights of the light-house and the building.
(ii) Distance between the light-house and the building.
(ii) Distance between light-house and building = 34.64 m.]
Or
The height of a house students a right angle at the opposite window. The angle of elevation of the window from the base of the house is 60°. If the width of the road is 6 m. Find the height of the house.

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136. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60° and the angle of depression of the point A from the top of the tower is 45°. Find the height of the tower

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137. As observed from the top of a light house, 100 m high above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30 to 60°. Determine the distances travelled by the ship during the period of observations.

115.46 m.

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138. The angle of elevation of a cloud from a point 200 m above the 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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139.

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and flag pole mounted on it.

From a building 60 metres high the angles of depression of the top and bottom of a lamp-post are 30° and 60° respectively. Find the distance between the lamp-post and building. Also find the difference of height between building and lamp-post.

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140.

Two pillars of equal height stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars on the roadway between the pillars, the elevations of the top of the pillars are 60° and 30°. Find the height of the pillar and the position of the point.

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevations of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and height of the hill.

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