Welcome to **AMBiPi (**Read as**: एम्बीपाई) (Amans Maths Blogs)**. JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get * JEE Main Math Previous Year Paper Height and Distance Questions Answer Keys Solutions*.

### JEE Mains Mathematics Height and Distance Questions Bank

**JEE Height and Distance Questions No:1**

The upper (3/4) th portion of a vertical pole subtends an angle tan^{-1} (3/5) 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

**[2003]**

**Option A**: 80 m

**Option B**: 20 m

**Option C**: 40 m

**Option D**: 60 m

**Show/Hide Answer Key**

**Option C: 40 m**

**JEE Height and Distance Questions No:2**

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 meters away from the tree the angle of elevation becomes 30° The breadth of the river is

**[2004]**

**Option A**: 60 m

**Option B**: 30 m

**Option C**: 40 m

**Option D**: 20 m

**Show/Hide Answer Key**

**Option D: 20 m**

**JEE Mathematics Height and Distance Questions No:3**

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 tower from A and B is 30°. The height of the tower is

**[2007]**

**Option A**: a / √3

**Option B**: a √3

**Option C**: 2a / √3

**Option D**: 2a√3

**Show/Hide Answer Key**

**Option A: a / √3**

**JEE Main Math Height and Distance Questions No:4**

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 the point A from a certain point C on the ground is 60°. He 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

**[2008]**

**Option A**: (7√3 / 2) (1/√3 – 1) m

**Option B**: (7√3 / 2) (√3 + 1) m

**Option C**: (7√3 / 2) (√3 – 1) m

**Option D**: (7√3 / 2) (1/√3 + 1) m

**Show/Hide Answer Key**

**Option B: (7 √3 / 2) (√3 + 1) m**

**Height and Distance JEE Questions No:5**

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is

**[2014]**

**Option A**: 2 sinα sinβ / sin (α – β)

**Option B**: sinα sinβ / cos (β – α)

**Option C**: 2 sin (β – α) / sinα sinβ

**Option D**: cos (β – α) / sinα sinβ

**Show/Hide Answer Key**

**Option A: 2 sin α sinβ / sin (α –**

**β**

**)**

**Height and Distance JEE Main Questions No: 6**

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. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is

**[2014]**

**Option A**: 20√2

**Option B**: 20 (√3 – 1)

**Option C**: 40 (√2 – 1)

**Option D**: N40 (√3 – √2)

**Show/Hide Answer Key**

**Option B: 20 ( √3 – 1)**

**Height and Distance Questions for JEE Mains Questions No: 7 **

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is ‘h’ and the distance of the foot of the smallest pole from O is ‘a’; then the distance between two consecutive poles, is

**[2015]**

**Option A**: h cosα – a sinα / 9 sinα

**Option B**: h sinα + a cosα / 9 sinα

**Option C**: h cosα – a sinα / 9 cosα

**Option D**: h sinα – a cosα / 9 cosα

**Show/Hide Answer Key**

**Option A: h cosα – a sinα / 9 sinα**

**Height and Distance Questions and Answers No:8**

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 ratio, AB: BC, is:

**[2015]**

**Option A**: 1:√3

**Option B**: 2:3

**Option C**: √3:1

**Option D**: √3:√2

**Show/Hide Answer Key**

**Option C: √3:1**

**Height and Distance Questions with Solutions No:9**

The angle of elevation of the top of a vertical tower from a point A, due cast of it is 45° The angle of elevation of the top of the same tower from a point B, due south of A is 30°.If the distance between A and B is 54√2 m, then the height of the tower (in metres), is

**[2016]**

**Option A**: 108

**Option B**: 36√3

**Option C**: 54√3

**Option D**: 54

**Show/Hide Answer Key**

**Option D: 54**

**JEE Mains Height and Distance Questions No: 10**

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 is 30°. 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 60°. Then the time taken (in minutes) by him, from B to reach the pillar, is

**[2016]**

**Option A**: 20

**Option B**: 5

**Option C**: 6

**Option D**: 10

**Show/Hide Answer Key**

**Option B: 5**

**JEE Mains Math Height and Distance Questions No:11**

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to

**[2002]**

**Option A**: 4/9

**Option B**: 6/7

**Option C**: 1/4

**Option D**: 2/9

**Show/Hide Answer Key**

**Option D: 2/9**

**Height and Distance Questions for JEE Questions No: 12**

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 twice the angle of elevation of the top of T_{2}, then the width (in m) of the road between the feet of the towers T_{1}, and T_{2}

**[2018]**

**Option A**: 20√2

**Option B**: 10√2

**Option C**: 10√3

**Option D**: 20√3

**Show/Hide Answer Key**

**Option D: 20 √3**

**Height and Distance Problems for Class 11 Questions No: 13**

An aeroplane flying at a constant speed, parallel to the horizontal ground, √3km above it, is observed at an elevation of 60° from a point on the ground. If, after five seconds, its elevation from the same point, is 30°, then the speed (in km/hr) of the aeroplane is

**[2018]**

**Option A**: 1500

**Option B**: 750

**Option C**: 720

**Option D**: 1440

**Show/Hide Answer Key**

**Option D: 1440**

**Height and Distance Problems for Class 12 Questions No: 14**

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 change from 30° to 45°, then after this, the time taken (in min) by the car to reach the foot of the tower, is

**[2018]**

**Option A**: 9 (1 + √3)

**Option B**: (9/2) (√3 – 1)

**Option C**: 18 (1 + √3)

**Option D**: 18 (√3 – 1)

**Show/Hide Answer Key**

**Option A: 9 (1 + √ 3)**

**Height and Distance Problems for Class 11 JEE Questions No: 15**

PQR is a triangular park with PQ = PR = 200 m. AT.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45°, 30° and 30°, then the height of the tower (in m) is

**[2018]**

**Option A**: 50

**Option B**: 100 √3

**Option C**: 50 √2

**Option D**: 100

**Show/Hide Answer Key**

**Option D: 100**

**Height and Distance Problems for Class 12 JEE Questions No: 16**

Consider a triangular plot ABC with sides AB = 7 m BC 5 m and CA=6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is

**[2019]**

**Option A**: (3/2) √21

**Option B**: (2/3) √21

**Option C**: 2 √21

**Option D**: 7 √3

**Show/Hide Answer Key**

**Option B: (2/3) √21**

**JEE Height and Distance Questions No:17**

ABC is a triangular park with AB = AC = 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 cot^{-1} (3√2) and cosec^{-1} (2√2) respectively, then the height of the tower (in metres) is

**[2019]**

**Option A**: 100 / 3√3

**Option B**: 10 √5

**Option C**: 20

**Option D**: 25

**Show/Hide Answer Key**

**Option C: 20**

**JEE Height and Distance Questions No:18**

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to:

**[2020]**

**Option A**: 100

**Option B**: 200√3

**Option C**: 400

**Option D**: 400√3

**Show/Hide Answer Key**

**Option C: 400**

**JEE Mathematics Height and Distance Questions No:19**

Two vertical poles AB = 15 m and CD = 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 BC and AD, then the height of P (in m) above the line AC is

**[2020]**

**Option A**: 20 / 3

**Option B**: 5

**Option C**: 10 / 3

**Option D**: 6

**Show/Hide Answer Key**

**Option D: 6**

**JEE Main Math Height and Distance Questions No:20**

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up on km to wards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is

**[2020]**

**Option A**: √3 – 1 / √3 + 1

**Option B**: √3 + 1 / √3 – 1

**Option C**: 1 / √3 – 1

**Option D**: 1 / √3 + 1

**Show/Hide Answer Key**

**Option C: 1 / √3 – 1**

**Height and Distance JEE Questions No:21**

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 meters towards the top, up a slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans : 80**

**Height and Distance JEE Main Questions No: 22**

A ray of light coming from the point (2, 2√3) is incident at an angle 30° on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point

**[2020]**

**Option A**: (3, -1/√3)

**Option B**: (4, –√3/2)

**Option C**: (3, –√3)

**Option D**: (4, –√3)

**Show/Hide Answer Key**

**Option C: (3, – √3)**

**Height and Distance Questions for JEE Mains Questions No: 23**

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 432 km/hour, the angle of elevation changes to 30°. If the jet plane is flying at a constant height, then its height is

**[2021]**

**Option A**: 1800√3 m

**Option B**: 3600 √3 m

**Option C**: 2400 √3 m

**Option D**: 1200 √3 m

**Show/Hide Answer Key**

**Option D: 1200 √3 m**

**Height and Distance Questions and Answers No:24**

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 elevation of their tops to be complementary, then the height of the shorter pole (in meters) is

**[2021]**

**Option A**: 20√3

**Option B**: 25√3

**Option C**: 30

**Option D**: 25

**Show/Hide Answer Key**

**Option B: 25 √3**

**Height and Distance Questions with Solutions No:25**

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 the point, angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45°. Then the time taken (in seconds) by the boat from B to reach the base of the tower is

**[2021]**

**Option A**: 10√3

**Option B**: 10

**Option C**: 10 (√3 + 1)

**Option D**: 10 (√3 – 1)

**Show/Hide Answer Key**

**Option C: 10 (√3 + 1)**

**JEE Mains Height and Distance Questions No: 26**

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 the height (in meter) of the top most point of the balloon from the level of the observer’s eye is

**[2021]**

**Option A**: 8 (2 + 2√3 + √2)

**Option B**: 8 (√6 + √2 + √2)

**Option C**: 8 (√2 + 2 + √3)

**Option D**: 8 (√6 – √2 + 2)

**Show/Hide Answer Key**

**Option B: 8 (√6 + √2 + √2)**

**JEE Mains Math Height and Distance Questions No:27**

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 point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is

**[2021]**

**Option A**: 12√15

**Option B**: 12√10

**Option C**: 8√10

**Option D**: 6√10

**Show/Hide Answer Key**

**Option B: 12 √10**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |