Two ships are sailing in the sea on the two sides of a light house. The angle of

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Question
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

Correct Answer

273m

Height and Distance problems

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1. 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

2. 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)

3. From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?
Options
A. 720
B. 960
C. 840
D. 1030

4. 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

5. The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, then the actual height of the tree is
Options
A. 17 m
B. 27 m
C. 25 m
D. 30 m

6. 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

7. 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

8. 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)

10. 129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30�. The height of this cliff is
Options
A. 50?3 metre
B. 45?3 metre
C. 43?3 metre
D. 47?3 metre

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