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EXERCISE – 26

Q. 1. from the top of a cliff 92 m high, the angle of depression of a buoy is 20º. Calculate to the nearest metre, the distance of the buoy from the foot of the cliff.

Q. 2. A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60º. When he moves 50 m, away from the bank, he finds the angle of elevation to be 30º. Calculate :

1. The width of the river and
2. The height of the tree.

Q. 3. The shadow of a vertical tower AB on level ground is increased by 10 m, when the altitude of the sun changes from 45º to 30º. Find the height of the tower correct to 1/10 of a metre.

Q. 4.  Vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower ?

Q. 5. From a window, 10 m above the ground, the angle of elevation of the top of a tower is xº, where tanxº = 5/2 and angle of depression of the foot of the tower is yº, where tanyº = ¼ . Calculate the height of the tower.

Q. 6. A man standing on the ground which is on the same horizontal plane as the foot of a vertical pole of height 10m, at some distance from the man. The man’s eye is 2 m above the ground. He observes the angle of elevation of the top of the pole as xº, where tanxº = 2/5. Calculate :

1. The distance of the man from the pole and
2. The angle of elevation of the top of the pole in nearest degree when he is standing 15 m from the pole.

Q. 7. Two objects are on the same side of a tower 300 m high. When observed from the top of the tower, the angles of depression are found to be 45ºand 60º respectively. Find the distance between the two objects.

Q. 8. Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 m wide. From a point between them on the road, the angle of elevation of their tops are 30º and 60º. Find the position of the point and also the height of the poles. [Use √3 = 1.732]

Q. 9.  The angle of elevation of the top of a tower from two points P and Q at a distance 90 m and 40 m respectively, from the base and in the same straight line with it, are complementary. Find the height of the tower.

Q. 10. A man on the top of a vertical tower observes a car moving at uniform speed towards the tower. If it takes 12 minutes for the angle of depression to change from 30º to 45º, how soon, after this, will the car reach the tower ?

Q. 11. The angle of elevation of the top of a hill at the foot of the tower is 60º and the angle of elevation of the top of the tower from the foot of the hill is 30º. If the tower is 50 m high, find the height of the hill.

Q. 12. From a window 15 m high above the ground in a street, the angle of elevation and depression of the top and foot of another house on the opposite side of the street are 30º and 45º respectively. Show that the height of the opposite house is 23.66 m.(Take √3 = 1.732).

Q. 13. The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30º. On advancing 150 m towards the foot of the tower, the angle of elevation becomes 60º. Show that the height of the tower is 129.9m. (Use √3 = 1.732).

Q. 14. A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60ºand the angle of depression of the base of the hill as 30º. Calculate the distance of the hill from the ship and the height of the hill.

Q. 15. The angle of depression of the top and the bottom of a building 50 m high as observed from the top of a tower are 30º and 60º respectively. Find the height of the tower and also the horizontal distance between the building and the tower. (Use √3 = 1.73)

Q. 16. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 5 m. From a point on the plane the angles of elevation of the bottom and top of the flagstaff are respectively 30º and 60º. Find the height of the tower.  

Q. 17. From the top of a hill 200 m high, the angles of depression of the top and the bottom of a pillar are 30º and 60º respectively. Find the height of the pillar and its distance from the hill. (Use √3 = 1.73).

Q. 18. The angle of elevation of a jet plane from a point A on the ground is 60º. After a flight of 15 seconds, the angle of elevation changes to 30º. If the jet plane is flying at a constant height of 1500√3 m, find the speed of the plane.

Q. 19. The angle of elevation of a cloud from a point 200 m above the lake is 30º and the angle of depression of the reflection of the cloud in the lake is 60º. Find the height of the cloud.

Q. 20. 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 30º to 60º. Determine the distance traveled by the ship during the period of observation. (Use √3 = 1.732).