A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from th

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Question
A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from the wall. If the end of the ladder (resting on the wall) slides down 4m, then how far will its foot move away?
Options
A. 5 m
B. 8 m
C. 9 m
D. 10 m

Correct Answer

8 m

Height and Distance problems

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1. Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30 ? and 45 ? respectively. If the height of the tower is 50 m, the distance between the two men is (Take ?3 = 1.73)
Options
A. 136.5 m
B. 50 ?3 m
C. 100 ?3 m
D. 135.5 m

2. The shadow of a tower when the angle of elevation of the sun is 45�, is found to be 10 m longer than when it was 60� . The height of the tower is
Options
A. 5(?3 - 1) m
B. 5(?3 + 1) m
C. 10 (?3 - 1) m
D. 10 (?3 + 1) m

3. The angle of elevation of an aeroplane from a point on the ground is 45�. After flying for 15 seconds, the elevation changes to 30�. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/hr. is
Options
A. 600
B. 600 (?3 + 1)
C. 600 ?3
D. 600 (?3 - 1)

4. A boat is moving away from an observation tower. It makes an angle of depression of 60� with an observer's eye when at a distance of 50m from the tower. After 8 sec., the angle of depression becomes 30�. By assuming that it is running in still water, the approximate speed of the boat is
Options
A. 33 km/hr
B. 42 km/hr
C. 45 km/hr
D. 50 km/hr

5. The upper part of a tree broke at a certain height makes an angle of 60 � with the ground at a distance of 10 m. from its feet. The original height of the tree was
Options
A. 20?3 m.
B. 10?3 m.
C. 10(2+?3) m.
D. 10(2-?3) m.

6. The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45 and 30 deg respectively. Height of the flag is [taking ?3 = 1.732]
Options
A. 12 ?3 m
B. 15 m
C. 14.32 m
D. 12.68 m

7. A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45� and 60�, then the width of the river is
Options
A. (200 + 200/?3) m
B. (200 - 200/?3) m
C. 400 ?3 m
D. (400/?3) m

8. A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8?3 m from its foot and makes an angle of 30� with the horizontal. The height (in metre) of the post is
Options
A. 12
B. 16
C. 18
D. 24

9. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
Options
A. 4 m
B. 7 m
C. 9 m
D. 6 m

10. A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60� and 30�respectively. Distance between the two ships, in metres is
Options
A. 1000?3
B. 1000/?3
C. 500?3
D. 500/?3

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