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A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower and the angle of elevation of the top of the first tower from A or B is 30°. The height of the tower is

1) 2a / √3 2) 2a √3 3) a / √3 4) √3 Solution: (3) a / √3 Let OP be the tower. OAB forms an equilateral triangle. OA = OB = AB = a In... View Article

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 60. If the distance between the two houses is 6 m, then the height of the first house is

1) 8√3 m 2) 6√3 m 3) 4√3 m 4) None of these Solution: (1) 8 √3 m From the figure, ∠DBC = 60o, ∠ADB = 90o, ∠EDB = ∠DBC = 60o ∠ADB = ∠ADE... View Article

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30°. After walking 120 m towards it on level ground, the elevation is found to be 60°. Then, the height (in metres) of the object is

1) 120 2) 60√3 3) 120√3 4) 60 Solution: (2) 60 √3 tan 60o = h / d tan 30o = h / [d + 120] 3 = [d + 120] / d d = 60 h = 60 √3... View Article

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

1) 4/√3 2) √3/2 3) 2/√3 4) 2 Solution: (2) √3 / 2 In triangle BCD, √3 = h / x x = h / √3 tan 30o = h / [x + 1] 1 / √3 = h / [x + 1] (h... View Article

A flagpole stands on a building of height 450 ft and an observer on 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

1) 4/3√3 2) √3/2 3) 9/2 4) √3/5 5) (4√3+1)/6 Solution: (1) 4 / [3√3] In triangle DCE, tan 30o = 150 / CD CD = √3 * 150 In triangle... View Article

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 the height of the tower is

1) a tan α 2) a sin α 3) a sin 2α 4) a sin 3α Solution: (3) a sin 2α In triangle BCE, using sine rule, BE / [sin (180 - 3α)] = CE / [sin... View Article

The shadow of the tower standing on 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

1) 45 m 2) 45 √3 m 3) 45/√3 m 4) 45 [√3 / 2] m Solution: (1) 45 m x = (45) * (3 / 2) y = 45 * (1 / 2) x - y = 45... View Article

A round balloon of radius r subtends an angle ɑ at the eye of the observer, while the angle of elevation of its centre is β. The height of the centre of the balloon is

1) r cosec ɑ sin (β / 2) 2) r sin ɑ cosec (β / 2) 3) r sin (ɑ / 2) cosec (β) 4) r cosec (ɑ / 2) sin (β) Solution: (4) r cosec (ɑ / 2) sin (β)... View Article

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

1) 2000/√3 m 2) 1000/√3 m 3) 2000/√2 m 4) 1000√3 m Solution: (1) 2000 / √3 m In triangle AEC, tan 60o = 500 / d1 d1 = 500 / √3 m In... View Article

From the top of a hill h meters high, the angles of depressions of the top and the bottom of a pillar are α and β, respectively. The height (in metres) of the pillar is

1) h [tan β - tan α] / [tan β] 2) h [tan α - tan β] / [tan α] 3) h [tan α + tan β] / [tan β] 4) h [tan α + tan β] / [tan α] Solution: (1) h... View Article

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of point A from a certain point on the ground is 60°. It moves away from the pole along the line BC to a point D such that CD = 7 m. From D, the angle of elevation of the point A is 45°. Then, the height of the pole is

1) (7 √3 / 2) [1 / (√3 + 1)] m 2) (7 √3 / 2) [1 / (√3 - 1)] m 3) (7 √3 / 2) [(√3 + 1)] m 4) (7 √3 / 2) [(√3 - 1)] m Solution: (3) (7 √3 / 2)... View Article

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

1) [b sin α sin (γ - β)] / [sin (γ - α)] 2) [b sin α sin (γ - α)] / [sin (γ - β)] 3) [b sin α sin (γ - β)] / [sin (γ - α)] 4) [sin (γ - β)] /... View Article

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

1) (a2 + b2) / 2 2) (a2 + b2) 3) 2 (a2 + b2) 4) 4 (a2 + b2) Solution: (3) 2 (a2 + b2) OA = a, AB = b, DE = a + b, CE = b - a l = (a +... View Article

ABC is a triangular park with AB = AC = 100 m. A vertical tower is situated at the midpoint of BC. The angle of elevation, if the top of the tower at A and B are cot^-1 3√2 and cosec^-1 2√2, respectively. The height of the tower is

1) 16 m 2) 25 m 3) 50 m 4) 20 m Solution: (4) 20 m cosec β = 2 √2 cot ɑ = 3 √2 x / h = 3 √2 --- (i) h / (√104 - x2) = 1 / √7 --- (ii)... View Article

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

1) 50 m 2) 50√3 m 3) 50 (√3 - 1) m 4) 50 (1 - √3 / 3) m Solution: (4) 50 (1 - √3 / 3) m From the figure, BD = 50m, AE = h = height of... View Article

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 + 1) m, then the height of the tower is

1) (4√3)/2 m 2) (√3 + 3)/2 m 3) (3 - √3)/ 2 m 4) √3/2 m 5) √3 + 1m Solution: (3) (3 - √3) / 2 m From the figure, PQ is the tower and... View Article

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

1) √3 : 1 2) √3 : 2 3) 1 : 2 4) 2 : √3 Solution: (1) √3 : 1 In triangle EDA, tan 30o = ED / AD 1 / √3 = ED / AD = h / AD AD = h √3 In... View Article

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

1) ab 2) √ab 3) √(a/b) 4) √(b/a) Solution: (2) √ab In triangle ABC, tan θ = h / a h = a tan θ --- (i) In triangle ADB, tan (90 - θ) =... View Article

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 some time, the angle of depression becomes 60°. The distance travelled by car during this is

1) 100√3 m 2) 200√3/3 m 3) 100√3 /3 m 4) 200√3 m Solution: (2) 200√3/3 m BC = 100 / tan 60o DB = 100 / tan 30o DC = 100 √3 - (100 /... View Article

A ladder rests against a wall so that it’s 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

1) 12√3 m 2) 12 m 3) 12/√3 m 4) None of these Solution: (2) 12 m √3 / 2 = 6 √3 / x x = 12 meters... View Article

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