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1.
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?
  • A.
    		 4 3  units  
  • C.
    12 units
  • E.
    None of these
  • B.
    8 units
  • D.
    Data inadequate
  • Answer & Explanation
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Answer : [D]
Explanation :
One of AB, AD and CD must have been given.
So, the data is inadequate.
 
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2.
A man on the top of a vertical observation tower observers a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?
  • A.
    14 min, 35 sec.
  • C.
    16 min. 23 s.
  • B.
    15 min 49 sec.
  • D.
    18 min. 5 sec.
  • Answer & Explanation
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Answer : [C]
Explanation :
Let AB be the tower and C and D be the two positions of the car.
Then,   ACB = 45°,   ADB = 30°  
Let AB = h, CD = x and AC = y.
AB
AC
 = tan 45° = 1  
 
 
h
y
 = 1
 
  y = h.    
AB
AD
 = tan 30° =
1
3
 
 
 
h
x + y
=
1
3
 
 
 
x + y = 3  h    
 
  x = (x + y) - y = 3  h - h = h( 3  - 1)  
Now, h( 3  - 1) is covered in 12 min.    
So, h will be covered in  
12
h( 3  - 1)
x h   =
12
( 3  - 1)
 min    
  =  
1200
73
   min. = 16 min. 23 sec.    
 
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3.
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
  • A.
    2.3 m
  • C.
    7.8 m
  • B.
    4.6 m
  • D.
    9.2 m
  • Answer & Explanation
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Answer : [D]
Explanation :
Let AB be the wall and BC be the ladder.
Then,  ACB = 60° and AC = 4.6 m.    
 
AC
BC
 = cos 60° =
1
2
   
 
  BC = 2 x AC = (2 x 4.6) m = 9.2 m.    
 
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4.
A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 metres from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
  • A.
    32 kmph
  • B.
    36 kmph
  • C.
    38 kmph
  • Answer & Explanation
  • Report
Answer : [A]
Explanation :
Let AB be the tower and C and D be the two positions of the boats.
Then,  ACB = 45°,  ADB = 30° and AC = 60 m.    
Let AB = h.
Then,
AB
AC
 = tan 45° = 1
 
  AB = AC
 
  h = 60 m.
     
And,
AB
AD
 = tan 30° =
1
3
 
 
 
AD = (AB x 3   ) = 60 3  m  
   
 
  CD = (AD - AC) = 60( 3  - 1) m.  
Hence, required speed =  
60 ( 3  - 1)
5
   m/s = (12 x 0.73) m/s        
=    12 x 0.73 x
18
5
   km/hr = 31.5 km/hr  
  = 32 km/hr.  
 
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5.
From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m hight, the distance of point P from the foot of the tower is:
  • A.
    149 m
  • C.
    173 m
  • B.
    156 m
  • D.
    200 m
  • Answer & Explanation
  • Report
Answer : [C]
Explanation :
Let AB be the tower. Then,  APB = 30° and AB = 100 m    
AB
AP
 = tan 30° =
1
3
 
 
 
AP = (AB x 3   ) = 100 3  m  
   
  = (100 x 1.73) m = 173 m.        
 
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