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CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 12 - MCQExams.com

A, B, C are three collinear points on the ground such that B lies between A and C and AB=10 m. If the angles of elevation of the top of a vertical tower standing at C are respectively 30 and 60 as seen from A and B, then the height of the tower is:
  • 53 m
  • 5 m
  • 1033 m
  • 2033 m
The angle of elevation of the top of a tower from a point A on the ground is 300. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 600. The height of the tower is : 
  • 3m
  • 53m
  • 103m
  • 203m
The angles of elevation of the top of a tower from two points A and B lying on the horizontal plane through the foot of the tower are respectively 450 and 300. If A and B are on the same side of the tower and AB=48metre, then the height of the tower is: 
  • 24(3+1) metre
  • 24 metre
  • 142 metre
  • 96 metre
At a point A, the angle of elevation of a tower of a lower is such that its tangent is   512;   on walking 120 meters nearer the tower the tangent of the angle of elevation  is 34. The height of the tower is : 
  • 225 meters
  • 200 meters
  • 230 metres
  • None of these
A man is walking towards a vertical pillar in a straight path, at uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60o. Then the time taken(in minutes) by him, from B to reach the pillar, is?
  • 6
  • 10
  • 20
  • 5
To cross a river a person covers a straight forward distance of 325 m along a bridge over the river. If bridge subtends 30o angle with edge of the river, find the width of the river?
  • 152.5
  • 155
  • 165
  • 162.5
In a storm, a tree got broken by the wind whose top meets the ground at an angle of 30o, at a distance of 30 meters from the root. What was the height of the tree before breaking?
  • 30 m
  • 303 m
  • 60 m
  • 603 m
The angles of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are respectively 15 and 30. If A and B are on the same side of the tower and AB = 48 m, Then the height of the tower is:
  • 243 m
  • 24 m
  • 242 m
  • 96 m
The shadow of a tree is 173 m. If the height of the tree is 17 m, then the sun's altitude is :
  • 30
  • 45
  • 60
  • 90
A tower substends an angle of 30o at a point on the same level as the foot of the tower. At a second point, h meter above first, point the depression of the foot of the tower is 60o, the horizontal distance of the tower from the point is _________________.
  • h cos60o
  • (h/3) cot30o
  • (h/3) cot60o
  • h cot30o
On the level ground, the angle of elevation of the top of angle nearer to it the angle of elevation becomes 60. The height is _________________.

  • 10m
  • 15m
  • 20m
  • none
If a tower 30 m high, casts a shadow 103 m long on the ground, then what is the angle of elevation of the sun?
  • 60o
  • 30o
  • 45o
  • 90o
An airplane flying horizontally at a height of 25003 m above that ground, is observed to be at an angle of elevation 60 from the ground. After a flight of 25 sec the angle of elevation is 30. Find the speed of the plane in  m/sec.
  • 100 m/sec
  • 200 m/sec
  • 300 m/sec
  • 400 m/sec
A chinny of 20 mt height, standing on the top of a building subtends an angle whose tangent is 16 at a distance of 70 mt from the foot of the building. The height of the building is 
  • 50 mt
  • 100 mt
  • 13.749 mt
  • 803mt
The angles of elevation of the top of a mountain from two points A and B on a horizontal line are 150 and 750.If AB=650 mt,then the height of the mountain is
  • 32533mt
  • 32532mt
  • 32433mt
  • 32432mt
The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h meter then, in meter, the height of the building is:
  • hcotxcotx+coty
  • hcotycotx+coty
  • hcotxcotxcoty
  • hcotycotxcoty
The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45 to 30. Then the height of the tower is:
  • 20(3+1)m
  • 24(3+1)m
  • 30(3+1)m
  • 30(31)m
The upper part of a tree broken over by the wind makes an angle of 30o with the ground, and the distance from the root to the point where the top of the tree meets the ground is 15 m. The present height of the tree is
  • 15 m
  • 103 m
  • 20 m
  • None of these
A ladder is inclined to a well at an angle α to the horizontal. Its foot is drawn up to a distance and as such, it slides a distance b along the well and makes angle β with the horizontal, then a is equal to:
  • b2tan(α+β)
  • btan(α+β)
  • btan(α+β2)
  • b2tan(α+β2)
A flagstaff 5 m high is placed on a building 25 m high. If the flag and building be subtend equal angels on the observer at a height 30 m, then the distance between observer and the top of flag is
  • 532
  • 523
  • 532
  • 523
The length of the shadow of a vertical tower on level ground increase  by 10 meters when the altitude of the sun changes from 45^o to 30^o. Then the height of the tower is:
  • 5\sqrt{3}
  • 10(\sqrt{3} + 1) meter
  • 5(\sqrt{3} + 1) meter
  • 10\sqrt{3} meter
A tower is 50\sqrt{3} m high. The angle of elevation of its top from a point 50 m away from its foot has measure............degree
  • 65
  • 60
  • 30
  • 15
A ladder leans against a wall making an angle of measure 60^\circ with the ground. If the foot of the ladder is 3 metre away from the wall, then the length of the ladder is ..... metre.
  • \dfrac{3}{2}
  • 3\sqrt{3}
  • 6
  • \dfrac{3\sqrt{3}}{2}
The tops of two towers of height x and y standing on a level round subtends angle of 30 and 60 respectively at the line joining their feet then x:y is.
  • 1 : 2
  • 2 : 1
  • 1 : 3
  • 3 : 1
The measure of the angle of elevation of sun increases from 30\ to\ 45, then the length of the shadow of a 100\ meter high building reduces by x\ meter. Then x is..... meter.
  • 100
  • 100\sqrt {3}
  • 100(\sqrt {3}-1)
  • \dfrac {100}{\sqrt {3}}
A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60^o to the horizontal. Determine the height of the balloon from the ground. Assume that there is no stack in the cable.
  • 175 m
  • 186 m
  • 190 m
  • 204 m
The upper \dfrac 34 ^{th} portion of a vertical pole subtends an angle \tan^{-1} \bigg(\dfrac 35\bigg) at a point in the horizontal plane through its foot and at a distance 40\ m from the foot. A possible height of the vertical pole is:
  • 40 m
  • 60 m
  • 80 m
  • 20 m
A 80 m long ladder is leaning on a wall. If the ladder makes an angle of 45^o with the ground, find the distance of the ladder from the wall.
  • 40\sqrt2 \ m
  • 20 \sqrt 3 \ m
  • 50 \sqrt 3 \ m
  • None of these
A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression to change from 30^{\circ} to 45^{\circ} : then after this , the time taken (in min) by the car to reach the foot of the tower, is 
  • 9(1+\sqrt{3})
  • 18(1+\sqrt{3})
  • 27(1+\sqrt{3})
  • 18(1+\sqrt{9})
A flag staff of height 'h' stands in the centre of a rectangular field and subtends angle of 15^{o} and 45^{o} at the mid point of its sides. Find the distance between them 
  • h\sqrt{2+\sqrt{3}}
  • 2h\sqrt{2+\sqrt{3}}
  • 4h\sqrt{2+\sqrt{3}}
  • 3h\sqrt{2+\sqrt{3}}
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