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Heights and Distances — JEE Main & Advanced Mathematics PYQs

137 previous year questions from Heights and Distances with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

137 questionsMathematicsSolutions on every page
1

The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower is 45 ° and from the feet of another person standing due west of the

JEE Main 2023 Solution View → 2

From the top A of a vertical wall A B of height 30 m , the angles of depression of the top P and bottom Q of a vertical tower P Q are 15 ∘ and 60 ∘ respectively, B and

JEE Main 2023 Solution View → 3

The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is cos - 1 3 13 . If the distance of

JEE Main 2022 Solution View → 4

A horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that ∠ P A O = ∠ P B O = 15 ° and &#8

JEE Main 2022 Solution View → 5

The angle of elevation of the top P of a vertical tower P Q of height 10 from a point A on the horizontal ground is 45 ° . Let R be a point on A Q and from a point B , vertica

JEE Main 2022 Solution View → 6

Let a vertical tower A B of height 2 h stands on a horizontal ground. Let from a point P on the ground a man can see upto height h of the tower with an angle of elevation 2 α

JEE Main 2022 Solution View → 7

A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that Q R = 15 m . If from a point A on the ground the angle of

JEE Main 2022 Solution View → 8

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60 ° . The pole subtends an angle 30 ° at the top of the tower. Then the heigh

JEE Main 2022 Solution View → 9

Let A B and P Q be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q , which are feet of these two poles. Let π 8 and θ be the angles

JEE Main 2022 Solution View → 10

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a

JEE Main 2021 Solution View → 11

Two poles A B of length a metres and C D of length a + b ( b ≠ a ) metres are erected at the same horizontal level with bases at B and D . If B D = x and tan ∠ A C B =

JEE Main 2021 Solution View → 12

A spherical gas balloon of radius 16 meter subtends an angle 60 ° at the eye of the observer A while the angle of elevation of its center from the eye of A is 75 ° . Then

JEE Main 2021 Solution View → 13

A pole stands vertically inside a triangular park A B C . Let the angle of elevation of the top of the pole from each corner of the park be π 3 . If the radius of the circumci

JEE Main 2021 Solution View → 14

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A , with uniform speed. At that point, angle of depression of the boat with the

JEE Main 2021 Solution View → 15

The angle of elevation of a jet plane from a point A on the ground is 60 ° . After a flight of 20 seconds at the speed of 432 km / hour , the angle of elevation changes to 30

JEE Main 2021 Solution View → 16

Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of

JEE Main 2021 Solution View → 17

The angle of elevation of the summit of a mountain from a point on the ground is 45 ° . After climbing up one km towards the summit at an inclination of 30 ° from the gro

JEE Main 2020 Solution View → 18

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45 ° . After walking a distance of 80 mete

JEE Main 2020 Solution View → 19

The angle of elevation of a cloud C from a point P , 200 m above a still take is 30 o . If the angle of depression of the image of C in the lake from the point P is 60 o , then P C

JEE Main 2020 Solution View → 20

Two vertical poles A B = 15 m and C D = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of B C and A D , then th

JEE Main 2020 Solution View → 21

A flag - staff of 5 meters high stands on a building of 25 meters height. For an observer at a height of 30 meters, the flag-staff and the building subtend equal angles. The distan

NTA Abhyas JEE Main 2020 Solution View → 22

A B is a vertical tower. The point A is on the ground and C is the middle point of A B . The part C B subtend an angle α at a point P on the ground. If A P = n A B , then the corre

NTA Abhyas JEE Main 2020 Solution View → 23

A tower subtends angles α , 2 α and 3 α , respectively, at points A , B and C all lying on a horizontal line through the foot of the tower. If A B B C = 1 + p cos ( p α ) , then th

NTA Abhyas JEE Main 2020 Solution View → 24

A ladder 5 m long leans against a vertical wall. The bottom of the ladder is 3 m from the wall. If the bottom of the ladder is pulled 1 m farther from the wall, how much does the t

NTA Abhyas JEE Main 2020 Solution View → 25

A tower T 1 of height 60 m is located exactly opposite to a tower T 2 of height 80 m on a straight road. From the top of T 1 , if the angle of depression of the foot of T 2 is twic

NTA Abhyas JEE Main 2020 Solution View → 26

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O .

NTA Abhyas JEE Main 2020 Solution View → 27

When the elevation of the sun changes from 45 o to 30 o , the shadow of a tower increases by 60 units, then the height of the tower is

NTA Abhyas JEE Main 2020 Solution View → 28

A chimney of 20 m height standing on the top of a building subtends an angle whose tangent is 1 6 at a distance of 70 m from the foot of the building, then the height of building i

NTA Abhyas JEE Main 2020 Solution View → 29

The length of the shadows of a vertical pole of height h , thrown by the sun's rays at three different moments are h , 2 h and 3 h . The sum of the angles of elevation of the rays

NTA Abhyas JEE Main 2020 Solution View → 30

Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as 45 o and 30 o respectively. If the height of the tower is 40 m , then

NTA Abhyas JEE Main 2020 Solution View → 31

The angle of elevation of a cloud from a point 250   m above a lake is 15 o and angle of depression of its reflection in the lake is 45 o . The height of the cloud is

NTA Abhyas JEE Main 2020 Solution View → 32

If the angles of elevation of the top of a tower from three collinear points A , B and C on a line leading to the foot of the tower are 30 ° , 45 ° and 60 ° respectively, then the

NTA Abhyas JEE Main 2020 Solution View → 33

The angle of 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

NTA Abhyas JEE Main 2020 Solution View → 34

P Q R is a triangular park with P Q = P R = 200   m . A TV tower stands at the mid-point of Q R . If the angles of elevation of the top of the tower from P , Q and R are 45 o

NTA Abhyas JEE Main 2020 Solution View → 35

A flagstaff stands vertically on a pillar, the height of the flagstaff being double the height of the pillar. A man on the ground at a distance finds that both the pillar and the f

NTA Abhyas JEE Main 2020 Solution View → 36

A harbour lies in the direction 60 o south-west from a fort and at a distance of 30 km from it. A ship sets out from the harbour at noon and sails due east at 10 km/hour, then the

NTA Abhyas JEE Main 2020 Solution View → 37

The angular depressions of the top and the foot of a tower, as seen from the top of a second tower which is 150 meters high and standing on the same level as the first, are t a n -

NTA Abhyas JEE Main 2020 Solution View → 38

A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100   m further from the first point in line with the tower, it sub

NTA Abhyas JEE Main 2020 Solution View → 39

If a tower subtends equal angles at four points P , Q , R and S that lie in a plane containing the foot of the tower, then which of the following statements is always true (here, t

NTA Abhyas JEE Main 2020 Solution View → 40

An aeroplane flying horizontally 1   km above the ground is observed at an elevation of 60 o and after 10 seconds the elevation is observed to be 30 o . The uniform speed of t

NTA Abhyas JEE Main 2020 Solution View → 41

Two poles standing on horizontal ground are of heights 10 meters & 40 meters respectively. The line joining their tops makes an angle of 30 o with the ground. Then the distance (in

NTA Abhyas JEE Main 2020 Solution View → 42

Two vertical poles of height 10  m and 40  m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each p

NTA Abhyas JEE Main 2020 Solution View → 43

A pole stands vertically in the center of a square. When 45 o is the elevation of the sun, the tip of its shadow just reaches the side of the square and is at a distance of 30 mete

NTA Abhyas JEE Main 2020 Solution View → 44

If from the top of a tower 80 meters high the angles of depression of the top and bottom of a house are 30 o and 45 o respectively, then the height of the house is

NTA Abhyas JEE Main 2020 Solution View → 45

A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 300 ft apart. When above A it has an altitude of 45 o as seen from B . When abo

NTA Abhyas JEE Main 2020 Solution View → 46

The angle of elevation of a cloud from a point 10 meters above the surface of a lake is 30 o and the angle of depression of its reflection from that point is 60 o . Then the height

NTA Abhyas JEE Main 2020 Solution View → 47

A tower A B leans towards west making an angle α with the vertical. The angular elevation of B , the top most point of the tower, is 6 0 o as observed from a point C due east of A

NTA Abhyas JEE Main 2020 Solution View → 48

Two poles of height 10 meters and 20 meters stand at the centres of two circular plots which touch each other externally at a point and the two poles subtend angles 3 0 o and 6 0 o

NTA Abhyas JEE Main 2020 Solution View → 49

A tower subtends an angle of 6 0 o at a point on the same level as the foot of the tower and at a second point just 10 meters above the first point the angle of depression of the f

NTA Abhyas JEE Main 2020 Solution View → 50

A pole is situated at the centre of a regular hexagonal park. The angle of elevation of the top of the vertical pole when observed from each vertex of the hexagon is π 3 . If the a

NTA Abhyas JEE Main 2020 Solution View → 51

An isosceles triangle made of wood of base 10 feet and height 8 feet is placed vertically with its base on the ground and vertex directly above it. If the triangle faces the sun wh

NTA Abhyas JEE Main 2020 Solution View → 52

Two straight roads O A and O B intersect at O . A tower is situated within the angle formed by them and subtends angles of 45 o and 30 o at the points A and B where the roads are n

NTA Abhyas JEE Main 2020 Solution View → 53

A stationary balloon is observed from three points A ,   B and C on the plane ground and is found that its angle of elevation from each point is 60 o . If ∠ A B C = 3 0

NTA Abhyas JEE Main 2020 Solution View → 54

A tower subtends angles α , 2 α and 3 α respectively at points, A , B and C (all points lying on the same side on a horizontal line through the foot of the tower), then the value o

NTA Abhyas JEE Main 2020 Solution View → 55

Two ships are sailling in the sea on the two sides of a lighthouse. If the distance between the ships is 10 3 + 1 meters and their angle of elevations of the top of the lighthouse

NTA Abhyas JEE Main 2020 Solution View → 56

The tops of two poles of heights 40 m and 25 m are connected by a wire. If the wire makes an angle 3 0 o with the horizontal, then the length of the wire is

NTA Abhyas JEE Main 2020 Solution View → 57

A person standing at the foot of a tower walks a distance of 3 meters from the tower and observes that the angle of elevation of the top of the tower is 30 o . He then walks a dist

NTA Abhyas JEE Main 2020 Solution View → 58

From the top of a tower, of 100 m height, the angles of depression of two objects, 200 3 m apart on the horizontal plane on a line passing through the foot of the tower and on the

NTA Abhyas JEE Main 2020 Solution View → 59

A tower leans towards west making an angle α with the vertical. The angular elevation of B , the top most point of the tower, is 75 o as observed from a point C due east of A

NTA Abhyas JEE Main 2020 Solution View → 60

The angular elevation of tower C D at a point A due south of it is 60 o and at a point B due west of A , the elevation is 3 0 o . If A B = 5 k m , then the height of the tower is (

NTA Abhyas JEE Main 2020 Solution View → 61

An observer finds that the angular elevation of a tower is θ . On advancing 3 m towards the tower, the elevation is 45 o and on advancing 2 m further more towards the tower, the el

NTA Abhyas JEE Main 2020 Solution View → 62

Two vertical poles A L and B M of heights 25 m and 100 m respectively stand apart on a horizontal plane. If A , B be the feet of the poles and A M and B L intersect at P , then the

NTA Abhyas JEE Main 2020 Solution View → 63

If from the top of a tower, 60 metres high, the angles of depression of the top and floor of a house are 30 o and 60 o respectively, then the height (in metres) of the house is

NTA Abhyas JEE Main 2020 Solution View → 64

Each side of a square subtends an angle of 60 ° at the top of a tower 5 meters high standing at the center of the square. If a meters is the length of each side of the square, then

NTA Abhyas JEE Main 2020 Solution View → 65

An isosceles triangle of wood of base 10 feet and height 8 3 feet is placed vertically with its base on the ground and vertex directly above. The triangle faces the sun whose altit

NTA Abhyas JEE Main 2020 Solution View → 66

Two vertical poles A L and B M of height 4 m and 16 m respectively stand apart on a horizontal plane. If A , B be the feet of the poles and A M and B L intersect at P , then the he

NTA Abhyas JEE Main 2020 Solution View → 67

Two straight roads O A and O B intersect at O . A tower is situated within the angle formed by them and subtends angles of 45 o and 30 o at the points A and B where the roads are n

NTA Abhyas JEE Main 2020 Solution View → 68

The tops of two poles of height 40 m and 25 m are connected by a wire of length 30 2 3 - 1 m . If the wire makes an angle α with the horizontal, then the value of 2 sin α is equal

NTA Abhyas JEE Main 2020 Solution View → 69

A flagstaff stands vertically on a pillar, the height of the flagstaff being triple the height of the pillar. A man on the ground at a distance finds that both the pillar and the f

NTA Abhyas JEE Main 2020 Solution View → 70

A ladder rests against a vertical wall at an angle α to the horizontal. If the foot is pulled away through a distance 2 m , then it slides a distance 5 m down the wall, finally mak

NTA Abhyas JEE Main 2020 Solution View → 71

A man is walking towards a vertical pillar in a straight path at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar

NTA Abhyas JEE Main 2020 Solution View → 72

Consider a cubical hall A B C D P Q R S with each side 20 m and base as A B C D . If G is the center of the wall B C R Q and T is the midpoint of the side A B , then the angle of e

NTA Abhyas JEE Main 2020 Solution View → 73

Two poles standing on a horizontal ground are of heights x meters and 40 meters respectively. The line joining their tops makes an angle of 30 o with the ground and the distance be

NTA Abhyas JEE Main 2020 Solution View → 74

A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100 m further in line with the tower, it subtends an angle of 30 o at th

NTA Abhyas JEE Main 2020 Solution View → 75

At the foot of the mountain, the angle of elevation of its summit is 45 o , after ascending 1000   m towards the mountain up a slope of 30 o inclination, the angle of elevatio

NTA Abhyas JEE Main 2020 Solution View → 76

A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 10 f t apart. When above A the balloon has an angle of elevation of 60 o as see

NTA Abhyas JEE Main 2020 Solution View → 77

A tower subtends an angle 75 o at a point on the same level as the foot of the tower and at another point, 10 meters above the first, the angle of depression of the foot of the tow

NTA Abhyas JEE Main 2020 Solution View → 78

A person standing at point P sees angle of elevation of the top of a building, whose base is 50 meters away, to be 60 o . Another building whose base is 20 meters away from the bas

NTA Abhyas JEE Main 2020 Solution View → 79

Two poles of height a meters and b meters stand at the centres of two circular plots which touch each other externally at a point and the two poles subtend angles of 30 o and 60 o

NTA Abhyas JEE Main 2020 Solution View → 80

Each side of a square subtends an angle of 60 o at the top of a tower 5 meters high standing in the center of the square. If a meters is the length of each side of the square, then

NTA Abhyas JEE Main 2020 Solution View → 81

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is 100 meters, sees the balloon at an angle of elevation of 30 o .

NTA Abhyas JEE Main 2020 Solution View → 82

A statue of height 4   m stands on a tower of height 10   m . The angle subtended by the statue at the eyes of an observer of height 2   m , standing at a distance o

NTA Abhyas JEE Main 2020 Solution View → 83

The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45 ° from a point A on the plane. Let B be the point 30 m vertically above the point

JEE Main 2019 Solution View → 84

A B C is a triangular park with A B = A C = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at, A and B are c o

JEE Main 2019 Solution View → 85

Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15 ° with the ground. Then the distance ( in

JEE Main 2019 Solution View → 86

Two vertical poles of height, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the

JEE Main 2019 Solution View → 87

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30 o and the angle of depression of reflection of the could in the lake from P be 60 o , then the

JEE Main 2019 Solution View → 88

Consider a triangular plot A B C with sides A B = 7 m , B C = 5 m and C A = 6 m . A vertical lamp-post at the mid-point D of A C subtends an angle 30 ° at B . The height (in m

JEE Main 2019 Solution View → 89

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 of the car to c

JEE Main 2018 Solution View → 90

A tower T₁ of height 60 ~m is located exactly opposite to a tower T₂ of height 80 ~m on a straight road. From the top of T₁ , if the angle of depression of the foot of T₂ is twice

JEE Main 2018 Solution View → 91

An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 ~km above it, is observed at an elevation of 60^ from a point on the ground. If, after five seconds, i

JEE Main 2018 Solution View → 92

An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it is observed at an elevation of 60 ° from a point on the ground. If after five seconds

JEE Main 2018 Solution View → 93

P Q R is a triangular park with P Q = P R = 200 m . A T.V. tower stands at the mid-point of Q R . If the angles of elevation of the top of the tower at P , Q and R are respectively

JEE Main 2018 Solution View → 94

Let a vertical tower A B have its end A on the level ground. Let C be the mid-point of A B and P be a point on the ground such that A P = 2 A B . If ∠ B P C = β , then t

JEE Main 2017 Solution View → 95

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45 o . The angle of elevation of the top of the same tower from a point B, due south of A is

JEE Main 2016 Solution View → 96

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pilla

JEE Main 2016 Solution View → 97

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of

JEE Main 2015 Solution View → 98

If the angles of elevation of the top of a tower from three collinear points A , B and C on a line leading to the foot of the tower are 30 ° , 45 ° and 60 ° respecti

JEE Main 2015 Solution View → 99

Two ships A and B are sailing straight away from a fixed point O along routes such that AOB is always 120^ . At a certain instance, OA =8 ~km , OB =6 ~km and the ship A is sailing

JEE Main 2014 Solution View → 100

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be . After moving a distance 2 metres from P towards the foot of the t

JEE Main 2014 Solution View → 101

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45 ° . It flies off horizontally straight away from the point O . A

JEE Main 2014 Solution View → 102

A B C D is a trapezium such that A B and C D are parallel and B C ⊥ C D . If ∠ A D B = θ , B C = p and C D = q , then A B is equal to

JEE Main 2013 Solution View → 103

If two vertical poles 20 ~m and 80 ~m high stand apart on a horizontal plane, then the height (in m ) of the point of intersection of the lines joining the top of each pole to the

JEE Main 2012 Solution View → 104

A B is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^ . He moves aw

JEE Main 2008 Solution View → 105

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that A B(=a) subtends an angle of 60^ at the foot of the tower, and the ang

JEE Main 2007 Solution View → 106

A lizard, at an initial distance of 21 ~cm behind an insect, moves from rest with an acceleration of 2 ~cm / s ^2 and pursues the insect which is crawling uniformly along a straigh

JEE Main 2005 Solution View → 107

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60^ and when he retires 40 meter away from t

JEE Main 2004 Solution View → 108

A particle moves towards east from a point A to a point B at the rate of 4 ~km / h and then towards north from B to C at the rate of 5 ~km / h . If A B=12 ~km and B C=5 ~km , then

JEE Main 2004 Solution View → 109

The upper 3 4 th portion of a vertical pole subtends an angle ⁻¹ 3 5 at a point in the horizontal plane through its foot and at a distance 40 ~m from the foot.

JEE Main 2003 Solution View → 110

A vertical tower stands on a horizontal ground. Two points P and Q are located on the ground due East and due North of the tower, respectively. The angles of elevation of the top o

JEE Main Solution View → 111

A vertical pole stands at a point O on the horizontal ground. A person at point A , due South of the pole, observes the angle of elevation of the top of the pole to be 60^ . The pe

JEE Main Solution View → 112

ABC is a triangular park with a right angle at B . A vertical tower is situated at the corner B . The length of the hypotenuse AC is 150 m. If the angles of elevation of the top of

JEE Main Solution View → 113

A vertical pole stands at the center of a regular hexagonal field. The angle of elevation of the top of the pole from any vertex of the hexagon is , where = 2 . If the angle of ele

JEE Main Solution View → 114

A hot air balloon is rising vertically upwards at a constant uniform speed. An observer is standing on the horizontal ground at a fixed distance from the launch pad. Initially, the

JEE Main Solution View → 115

The angle of elevation of the top of a vertical tower from a point on the horizontal ground is 45^ . From this point, an observer walks a distance d meters towards the tower up a s

JEE Main Solution View → 116

A spherical balloon of radius 10 m subtends an angle of 60^ at the eye of an observer standing at a height h above the surface of a lake. The angle of elevation of the center of th

JEE Main Solution View → 117

A vertical pole stands at a point O on horizontal ground. Two observation points A and B are located on the ground such that A is due West of O , and B is due South of O . The angl

JEE Main Solution View → 118

A vertical tower stands at an arbitrary point inside a rectangular field ABCD . The angles of elevation of the top of the tower from the corners A , B , and C are 30^ , 45^ , and 6

JEE Main Solution View → 119

A vertical tower stands inside a triangular field whose side lengths are 6 m, 8 m, and 10 m. The angles of elevation of the top of the tower from the three corners of the field are

JEE Main Solution View → 120

A hoarding of height 5 m is mounted on a vertical wall. The bottom of the hoarding is at a height of 4 m above the horizontal eye level of an observer. The distance from the wall a

JEE Main Solution View →
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