A man standing on the bank of river observes that the angle subtended by a tree

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Question
A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60�. When he retires 36 m from the bank, he finds that the angle is 30�. The breadth of the river is
Options
A. 15 m
B. 18 m
C. 16 m
D. 11 m

Correct Answer

18 m

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Height and Distance problems

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1. Two ships are sailing in the sea on the two sides of a light house. The angle of elevation of the top of the light house as observed from the two ships are 30� and 45� respectively. If the light house is 100m high, the distance between the two ships is :(take ?3=1.73)
Options
A. 173m
B. 200m
C. 273m
D. 300m

2. On a ground , there is a vertical tower with a flagpole on its top . At a point 9 m away from the foot of the tower , the angles of elevation of the top and bottom of the flagpole are 60� and 30� respectively . The height of the flagpole is
Options
A. 5?3 m
B. 6?3 m
C. 6?2m
D. 6?5 m

3. A tower is broken at a point P above the ground. The top of the tower makes an angle 60� with the ground at Q. From another point R on the opposite sideof Q angle of elevation of point P is 30�. If QR = 180 m, then what is the total height (in metres) of the tower?
Options
A. 90
B. 45?3
C. 45(?3+1)
D. 45(?3+2)

4. From a point P on a level ground , the angle of elevation to the top of the tower is 30� . If the tower is 100m high , the distance of point P from the foot of the tower is ( Take ?3 = 1.73)
Options
A. 149 m
B. 156 m
C. 173 m
D. 188 m

5. A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :
Options
A. 17 m
B. 16 m
C. 14 m
D. 15 m

6. A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30 deg. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?
Options
A. 210
B. 140?3
C. 210?3
D. 150

7. Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45 deg and 60 deg. If the height of the tree which makes 45 deg angle is 200 metres, then what will be the height (in metres) of the other tree?
Options
A. 200
B. 200?3
C. 100?3
D. 250

8. A Navy captain going away from a lighthouse at the speed of 4[(?3) ? 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60 to 45 deg. What is the height (in metres) of the lighthouse?
Options
A. 240?3
B. 480[(?3) ? 1]
C. 360?3
D. 280?2

9. From the top of a tower 60 mts high the angle of depression of the top and bottom of a pole are observed to be 45� and 60� respectively. If the pole and tower stand on the same plane, the height of the pole in meters is
Options
A. 60(?31)
B. 20(?31)
C. 20(3?3)
D. 20(?3+1)

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