The angles of elevation of the top of a tree 220 meters high from two points lie

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Question
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

Correct Answer

161.05

Height and Distance problems

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1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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)

8. 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

9. 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

10. The upper part of a tree broken over by the wind make an angle of 60 deg with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?
Options
A. 84.14
B. 93.3
C. 98.25
D. 120.24

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