JEE Questions for Maths Heights And Distances Quiz 1 - MCQExams.com

A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window is 64 m, then the distance between the two houses is
  • 48 m
  • 36 m
  • 54 m
  • 72 m
ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is θ, then tan θ is equal to
  • √6
  • 1/√6
  • √3/2
  • √2/2
A vertical pole PO is standing at the centre 0 of a square ABCD. If AC subtends an ∠ 90° at the top P of the pole, then the angle subtended by a side of the square at P is
  • 30°
  • 45°
  • 60°
  • None of these
The angles of elevation of the top of a tower at two points, which are at distances a and b from the foot in the same horizontal line and on the same side of the tower, are complementary. The height of the tower is
  • ab
  • √ab
  • √(a/b)
  • √(b/a)
Angles of elevation of the top of a tower from three points (collinear) A ,B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB to BC is
  • √3 : 1
  • √3 : 2
  • 1 : 2
  • 2 : √3
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°. The height of tower is
  • 50 m
  • 50√3 m
  • 50 (√3 -m
  • 50 (1 - √3/3 ) m
ABC is a triangular park with ,AB = AC = 100 m. A clock tower is situated at the mid-point of BC. The angle of elevation, if the top of the tower at A and B are cot-1 3 2 and cosec-12.6, respectively. The height of the tower is
  • 16 m
  • 25 m
  • 50 m
  • None of these
P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are 45° each. Then, the square of the distance between the tops of the poles is
  • (a2+b2)/2
  • a2 + b2
  • 2(a2 + b2)
  • 4(a2 + b2)
The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are 30° and 60°. If the height of the cliff is 500 m, then the diameter of the base of the cliff is
  • 2000/√3 m
  • 1000/√3 m
  • 2000/√2 m
  • 1000√3 m
A round balloon of radius r subtends an angle a at the eye of the observer, while the angle of elevation of its center is β. The height of the centre of balloon is

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The shadow of tower standing on a level ground is x meters long when the Sun\'s altitude is 30°, while it is y meters long when the altitude is 60°. If the height of the tower is 45.√3/2 m then x - y is equal to
  • 45 m
  • 45 √3 m
  • 45/√3 m
  • 45 . √3/2 m
The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are α, 2α and 3α, respectively. If AB = α, then height of the tower is
  • a tan α
  • a sin α
  • a sin 2α
  • a sin 3α
A flagpole stands on a building of height 450 ft and an observer on a level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is 30° and the height of the flagpole is 50 ft. If 0 is the angle of elevation of the top of the flagpole, then tanθ is
  • 4/3√3
  • √3/2
  • 9/2
  • √3/5
  • (4√3+1)/6
From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be 30° and 60°, respectively. The height (in km) at which the aeroplane is flying, is
  • 4/√3
  • √3/2
  • 2/√3
  • 2
A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is 60o. If the distance between the two houses is 6 m, then the height of the first house is
  • 8√3 m
  • 6√3 m
  • 4√3 m
  • None of these
The angle of elevation of top of a tower from a point on the ground is 30° and it is 60° when it is viewed from a point located 40 m away from the initial point towards the tower. The height of the tower is
  • - 20√3 m
  • √3/20 m
  • - √3/20 m
  • 20√3 m
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and height of the house is 6√3 in, then the length of the ladder is
  • 12√3 m
  • 12 m
  • 12/√3 m
  • None of these
A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After sometime, the angle of depression becomes 60°. The distance travelled by the car during this is
  • 100√3 m
  • 200√3/3 m
  • 100√3 /3 m
  • 200√3 m
From the top of a tower, the angle of depression of a point on the ground is 60°. If the distance of this point from the tower is 1/(√3+m, then the height of the tower is
  • (4√3)/2 m
  • (√3 + 3)/2 m
  • (3 - √3)/ 2 m
  • √3/2 m
  • √3 + 1m
The angle of elevation of the top of a hill from a point is α. After walking b meters towards the top up a slope inclined at an angle β to the horizon, the angle of elevation of the top becomes γ . Then, the height of the bill is

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