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Some Applications of Trigonometry

Short Answer Type

141. A vertical tower stands on a horizontal plane and its surmmounted by a vertical flagstaff of height 5 m. From a point on the plane the angles of elevation of bottom and top of the flagstaff are respectively 30° and 60°. Find the height of the tower.

2.5 m

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142.

The angles of depression of the top and the bottom of a building 50 m high as observed from the top of a tower are 30° and 60° respectively. Find the height of the tower and also the horizontal distance between the building and the tower.

The angle of elevation of the top of a tower as observed from a point on the ground is d and on moving α metres towards the tower the angle of elevation is β prove that the

height of the tower is $fraction numerator straight alpha space tan space straight d space. space tan space straight beta over denominator tan space straight beta space minus space tan space straight alpha end fraction$ .

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143. The angle of elevations of the top of a hill at the foot of the tower is 60° and the angle of elevations of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.

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144. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elecvation of 30°. A girl standing on the roof of 20 metre high building finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.

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145. A pole 5m high is fixed on the lop 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 point a from the top of the tower is 45°. Find the height of the tower.

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146. A window in a building is at a height of 10 m from the ground. The angle of depression of a poinl P on the ground from the window is 30°. The angle of elevation of the top of the building from the poinl P is 60°. Find the height of the building.

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147. A slatue 1.46 m tall, stands on the pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevaton of the top of the pedestal is 45. Find the height of the pedestal.

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148. A person standing on the bank of a river observed that the angle of elevation of the top of a tree standing on the opposite bank is 60°. when we moves 40m away from the bank, we finds the angle of elevation to be 30°. Find the height of the tree and Ihe width of the river.

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149. The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the jet is flying at a speed of 720 km/hr. find the constant height at which the jet is flying.

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150. The angle of elevations of a jet fighter from a point A on the ground is 60°. After a flight of 10 seconds, the angle of elevation changes to 30°. If the jet is flying at a speed of 402 km/hr, find the constant height at which the jet is flying.

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