A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60°. When he retreated 20m from the bank, he finds the angle to be 30°. Find the height of the tree and the breadth of the river.

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A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance of 30 meters from the roots. Find the whole height of the tree.

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The angles of elevation of the top of a tower from two points at distances p and q meters from the base and in the same straight line with it are complementary. Prove that the height of the tower is $\sqrt {pq}$

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At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12 . On walking 192 meters towards the tower, the tangent of the angle of elevation is 3/4. Find the height of the tower.

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A person 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

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A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the tower? Give your answer to the nearest second.

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The shadow of a flag – staff is three times as long as the shadow of the flag – staff when the sun rays meet the ground at an angle of 60

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An aeroplane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60

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Two pillars of equal height and on either side of a road, which is 100m wide. The angles of elevation of the top of the pillars are 60

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The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30

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If the angle of elevation of a cloud from a point h meters above a lake is $\alpha$ and the angle of depression of its reflection in the lake is $\beta$, prove that the height of the cloud is

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A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is $ \beta$. Prove that the height of the centre of the balloon is

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The angle of elevation of a cliff from a fixed point is $\theta$. After going up a distance of K meters towards the top of the cliff at an angle of $\phi$, it is found that the angle of elevation is $\alpha$. Show that the height of the cliff is meter

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The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40m vertically above X, the angle of elevation of the top is 45° Calculate the height of the tower.

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If the angle of elevation of a cloud from a point h metre above a lake is $\alpha$ and the angle of depression of its reflection in the lake be $\beta$, prove that the distance of the cloud from the point of observation is

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From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be $\alpha$ and $\beta$. Show that the height in miles of aeroplane above the road is given by

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A ladder rests against a wall at an angle $\alpha$ to the horizontal. Its foot is pulled away from the wall through a distance , so that its slides a distance b down the wall making an angle $\beta$ with the horizontal. Show that

A boy is standing on the ground and flying a kite with 100m of string at an elevation of 30°. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.

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Two boats approach a light house in mid- sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100m, find the height of the light house.

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From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be $\alpha$ and $\beta$. If the height of the light house be h meters and the line joining the ships passes through the foot of the light house, show that the distance between the ship is metres

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As observed from the top of a 150m tall light house, the angles of depression of two ships approaching it are 30° and °. If one ship is directly behind the other, find the distance between the two ships.

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This Class 10 Maths Important Questions for Application of Trigonometry with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.You can download in PDF form also using the below links

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Class 10 Maths Class 10 Science