The angle of elevation of an aeroplane as observed from a point 30 m above the t

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Question
The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30� and the angle of depression of the image of the aeroplane in the water of the lake is 60�. The height of the aeroplane from the water-surface of the lake is
Options
A. 60 m
B. 45 m
C. 50 m
D. 75 m

Correct Answer

60 m

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Height and Distance problems

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1. 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

2. 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

3. 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

4. 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

5. 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

6. The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are 30� and 45�. What is the distance (in metres) between the two points?
Options
A. 193.22
B. 144.04
C. 176.12
D. 161.05

7. The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30� and 60� respectively. What is the height (in metres) of building?
Options
A. 42
B. 20?3
C. 24?3
D. 48

8. The angle of elevation of an aeroplane from a point on the ground is 60 deg. After flying for 30 seconds, the angle of elevation changes to 30 deg. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?
Options
A. 50?3
B. 100?3
C. 200?3
D. 300?3

9. A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450?3 metres from point P observes that angle of elevation of the balloon is 60 deg. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?
Options
A. 4.25
B. 3.75
C. 4.5
D. 3.45

10. On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45 to 60 deg. What will be the height (in metres) of the building?
Options
A. 50(3 + ?3)
B. 100(?3 + 1)
C. 150
D. 100?3

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