- A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60
^{o}. When he retreated 20m from the bank, he finds the angle to be 30^{o}. Find the height of the tree and the breadth of the river. - A tree is broken by the wind. The top struck the ground at an angle of 30
^{o}and at a distance of 30 meters from the roots. Find the whole height of the tree. - 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 √pq
- 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.
- 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
^{o}. When he moves 40 meters away from the bank, he finds the angle of elevation to be 30^{o}. Find the height of the tree and the width of the river. - 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
^{o }to 45^{o}, how soon after this, will the car reach the tower? Give your answer to the nearest second. - 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
^{o}. Find the angle between the sun rays and the ground at the time of longer shadow. - 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
^{o}and 60^{o}. Find the width of the river. - 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
^{o}and 30^{o}at a point on the road between the pillars. Find the position of the point between the pillars and the height of each pillar. - The angle of elevation of a jet plane from a point A on the ground is 60
^{o}. After a flight of 30 seconds, the angle of elevation changes to 30^{o}. If the jet plane is flying at a constant height of 3600 √3m, find the speed of the jet plane. - If the angle of elevation of a cloud from a point h meters above a lake is α and the angle of depression of its reflection in the lake is β, prove that the height of the cloud is
- 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 β. Prove that the height of the centre of the balloon is
- The angle of elevation of a cliff from a fixed point is θ. After going up a distance of K meters towards the top of the cliff at an angle of φ, it is found that the angle of elevation is α . Show that the height of the cliff is meter

Answer

- H = 10√ 3 = 17.32M
- 51.96 m
- √pq m
- h=180m
- h = 34. 64m, width = 20m
- 16 minutes 23 seconds
- 30
^{o} - 315.4 meters
- Distance from 1
^{st}pillar = 25m, 2^{nd}= 75m, Height = 43.3m - 864km/hr

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