Height and Distance MCQ Questions & Answers

Height and Distance MCQs : This section focuses on the "Height and Distance". These Multiple Choice Questions (MCQs) should be practiced to improve the Height and Distance skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building, which casts a shadow of length 28.75 m under similar conditions ?

A. 14 cm

B. 13.5 cm

C. 12.5 cm

D. 11.4 cm

Question 2

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 metres from point P observes that angle of elevation of the balloon is 60 deg. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

A. 4.25

B. 3.75

C. 4.5

D. 3.45

Question 3

A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from the wall. If the end of the ladder (resting on the wall) slides down 4m, then how far will its foot move away?

A. 5 m

B. 8 m

C. 9 m

D. 10 m

Question 4

From the top of a platform 7 m high, the angle of elevation of a tower was 30 deg. If the platform was positioned 50√3 m away from the tower, how tall was the tower?

A. 57 m

B. 50 m

C. (25√3 + 7) m

D. 25√3 m

Question 5

From the top of a building, the angles of elevation and depression of top and bottom of a tower are 60 deg and 30 deg respectively. If the height of the building is 5m, then the height of the tower is

A. 20 m

B. 15 m

C. 10√3 m

D. 5√3 m

Question 6

The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

A. 63

B. 30

C. 25

D. 45

Question 7

The angle of depression of the foot of a building from the top of a tower 30 m away is 30 deg. How high is the tower?

A. 10√3 m

B. 20√3 m

C. 30 m

D. 20 m

Question 8

An observer 1.6 m tall is 203away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:

A. 21.6 m

B. 23.2 m

C. 24.72 m

D. None of these

Question 9

A kite is flying at a height of 50m. If the length of string is 100 m then the inclination of string to the horizontal ground in degree measures is

A. 90

B. 45

C. 60

D. 30

Question 10

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m

B. 200 m

C. 273 m

D. 300 m

Question 11

The angle of elevation of the top of a hill at the foot of the tower is 60 deg and the angle of elevation of the top of the tower from the foot of the hill is 30 deg. If the tower is 50 m high, what is the height of the hill?

A. 100 m

B. 120 m

C. 180 m

D. 150 m

Question 12

The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30° and 60° respectively. What is the height (in metres) of building?

A. 42

B. 20√3

C. 24√3

D. 48

Question 13

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m

B. 200 m

C. 273 m

D. 300 m

Question 14

The angle of elevation of a ladder leaning against a wall is 60 deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is

A. 2.3 m

B. 4.6 m

C. 9.2 m

D. 7.8 m

Question 15

The thread of a kite makes 60 deg angle with the horizontal plane. If the length of the thread be 80 m, then the vertical height of the kite will be

A. 40/√3 m

B. 80√3 m

C. 80 m

D. 40√3 m

Question 16

129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30°. The height of this cliff is

A. 50√3 metre

B. 45√3 metre

C. 43√3 metre

D. 47√3 metre

Question 17

From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?

A. 720

B. 960

C. 840

D. 1030

Question 18

The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is

A. 60 m

B. 45 m

C. 50 m

D. 75 m

Question 19

From the top of a platform 5 m high, the angle of elevation of a tower was 30 deg. If the platform was positioned 40√3 m away from the tower, how tall was the tower?

A. 40 m

B. 20√3 m

C. 30√3 m

D. 45 m

Question 20

A boat is moving away from an observation tower. It makes an angle of depression of 60° with an observer's eye when at a distance of 50m from the tower. After 8 sec., the angle of depression becomes 30°. By assuming that it is running in still water, the approximate speed of the boat is

A. 33 km/hr

B. 42 km/hr

C. 45 km/hr

D. 50 km/hr

Question 21

Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30 ̊ and 45 ̊ respectively. If the height of the tower is 50 m, the distance between the two men is (Take √3 = 1.73)

A. 136.5 m

B. 50 √3 m

C. 100 √3 m

D. 135.5 m

Question 22

A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30 deg. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

A. 210

B. 140√3

C. 210√3

D. 150

Question 23

The upper part of a tree broke at a certain height makes an angle of 60 ° with the ground at a distance of 10 m. from its feet. The original height of the tree was

A. 20√3 m.

B. 10√3 m.

C. 10(2+√3) m.

D. 10(2-√3) m.

Question 24

The angle of elevation of the sun, when the length of the shadow of a tree root(3) times the height of the tree, is:

A. 30 degree

B. 45 degree

C. 60 degree

D. 90 degree

Question 25

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

A. 7.5 km

B. 10.5 km

C. 12.5 km

D. 15 km

Question 26

From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of it's foot is at 45°, then the height of the tower is (√3=1.732)

A. 45.46 m

B. 45.64 m

C. 54.64 m

D. 54.46 m

Question 27

The height of a light house is 20 mts above sea level. The angle of depression (from the top of the lighthouse) of a ship in the sea is 30 deg. What is the distance of the ship from the foot of the light house?

A. 16 m

B. 20√3 m

C. 20 m

D. 30 m

Question 28

Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30 and 60 deg respectively. The distance between the persons is

A. 173.2m

B. 100m

C. 157.7m

D. 273.2m

Question 29

The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, then the actual height of the tree is

A. 17 m

B. 27 m

C. 25 m

D. 30 m

Question 30

Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45 deg and 60 deg. If the height of the tree which makes 45 deg angle is 200 metres, then what will be the height (in metres) of the other tree?

A. 200

B. 200√3

C. 100√3

D. 250

Question 31

From the top of a platform, the angle of elevation of a tower was 30 deg. The tower was 45 mts high and the horizontal distance between the platform and the tower was 40√3 m. What was the height of the platform?

A. 40 m

B. 5 m

C. 45√3 m

D. 20√3 m

Question 32

Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively the distance between two men is

A. 100 3m

B. 100m

C. 753m

D. 253m

Question 33

A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?

A. 6.2 m

B. 6.5 m

C. 6.8 m

D. 7.5 m

Question 34

The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60° . The height of the tower is

A. 5(√3 - 1) m

B. 5(√3 + 1) m

C. 10 (√3 - 1) m

D. 10 (√3 + 1) m

Question 35

A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30°respectively. Distance between the two ships, in metres is

A. 1000√3

B. 1000/√3

C. 500√3

D. 500/√3

Question 36

The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45 and 30 deg respectively. Height of the flag is [taking √3 = 1.732]

A. 12 √3 m

B. 15 m

C. 14.32 m

D. 12.68 m

Question 37

On a ground , there is a vertical tower with a flagpole on its top . At a point 9 m away from the foot of the tower , the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively . The height of the flagpole is

A. 5√3 m

B. 6√3 m

C. 6√2m

D. 6√5 m

Question 38

The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are 30° and 45°. What is the distance (in metres) between the two points?

A. 193.22

B. 144.04

C. 176.12

D. 161.05

Question 39

On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45 to 60 deg. What will be the height (in metres) of the building?

A. 50(3 + √3)

B. 100(√3 + 1)

C. 150

D. 100√3

Question 40

The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/hr. is

A. 600

B. 600 (√3 + 1)

C. 600 √3

D. 600 (√3 - 1)

Question 41

A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45° and 60°, then the width of the river is

A. (200 + 200/√3) m

B. (200 - 200/√3) m

C. 400 √3 m

D. (400/√3) m

Question 42

The height of a tower is 300 meters. When its top is seen from top of another tower,then the angle of depression is 60°. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower?

A. 88.24

B. 106.71

C. 92.15

D. 112.64

Question 43

Two poles of the height 15 m and 20 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

A. 11 m

B. 12 m

C. 13 m

D. 14 m

Question 44

The top and bottom of a tower were seen to be at angles of depression 30° and 60° from the top of a hill of height 100 m. Find the height of the tower ?

A. 42.2 mts

B. 33.45 mts

C. 66.6 mts

D. 58.78 mts

Question 45

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

A. Data inadequate

B. 8 units

C. 12 units

D. None of these

Question 46

Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

A. 6

B. 8

C. 9

D. 10

Question 47

A balloon is connected to a meteorological station by a cable of length 130 m, inclined at 60 deg to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in cable.

A. 110.32 m

B. 173 m

C. 163.28 m

D. 112.58 m

Question 48

A man is watching form the top of the tower a boat speeding away from the tower. The boat makes the angle of depression of 45 degree with the man's eye when at a distance of 60 metres from the tower. After 5 seconds the angle of depression becomes 30 degree. What is the approximate speed of the boat, assuming that it is running in still water ?

A. 22 Km/Hr

B. 28 Km/Hr

C. 32 Km/Hr

D. 36 Km/Hr

Question 49

The angle of elevation of a ladder leaning against a wall is 60 degree and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A. 2.3 m

B. 4.6 m

C. 7.8 m

D. 9.2 m

Question 50

The Top of a 15 metre high tower makes an angle of elevation of 60 degree with the bottom of an electric pole and angle of elevation of 30 degree with the top of pole. Find the height of the electric pole.

A. 7 metre

B. 8 metre

C. 9 metre

D. 10 metre

Question 51

A tower is 50 meters high.Its shadow is x metres shorter when the sun's altitude is 45° than when it is 30° . The value of x in metres is

A. 50√3

B. 50 (√3 - 1)

C. 50 (√3 + 1)

D. 50

Question 52

The height and the slant height of a right circular cone are 24 cm and 25 cm, respectively. Considering π as 22/7 , find the curved surface area of the said cone.

A. 550 cm2

B. 572 cm2

C. 528 cm2

D. 539 cm2

Question 53

A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is

A. 15 m

B. 18 m

C. 16 m

D. 11 m

Question 54

Two ships are sailing in the sea on the two sides of a light house. The angle of elevation of the top of the light house as observed from the two ships are 30° and 45° respectively. If the light house is 100m high, the distance between the two ships is :(take √3=1.73)

A. 173m

B. 200m

C. 273m

D. 300m

Question 55

An observer 1.6 m tall is 20 root(3) away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

A. 21.6 m

B. 23.2 m

C. 24.72 m

D. None of these

Question 56

The length of shadow of a tower is √3 times that of its length. The angle of elevation of the sun is

A. 45°

B. 30°

C. 60°

D. none

Question 57

From the top of a tower 60 mts high the angle of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. If the pole and tower stand on the same plane, the height of the pole in meters is

A. 60(√31)

B. 20(√31)

C. 20(3√3)

D. 20(√3+1)

Question 58

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :

A. 17 m

B. 16 m

C. 14 m

D. 15 m

Question 59

A vertical toy 18 cm long casts a shadow 8 cm long on the ground. At the same time a pole casts a shadow 48 m. long on the ground. Then find the height of the pole ?

A. 1080 cm

B. 180 m

C. 108 m

D. 118 cm

Question 60

If the length of the shadow of a vertical pole on the horizontal ground is √3 times its height, then the angle of elevation

A. 40 deg

B. 50 deg

C. 30 deg

D. 45 deg

Question 61

If an object travels at five feet per second, how many feet does it travel in one hour?

A. 30

B. 3000

C. 18

D. 1800

Question 62

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A. 2.3m

B. 4.6m

C. 7.8m

D. 9.2m

Question 63

A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8√3 m from its foot and makes an angle of 30° with the horizontal. The height (in metre) of the post is

A. 12

B. 16

C. 18

D. 24

Question 64

From a point C on a level ground, the angle of elevation of the top of a tower is 30 degree. If the tower is 100 meter high, find the distance from point C to the foot of the tower.

A. 170 meter

B. 172 meter

C. 173 meter

D. 167 meter

Question 65

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A. 149 m

B. 156 m

C. 173 m

D. 200 m

Question 66

The angle of elevation of a ladder leaning against a wall is 60 deg and the foot of the ladder is 4.2 m away from the wall. The length of the ladder is

A. 9.2 m

B. 11.4 m

C. 8.5 m

D. 13.5 m

Question 67

From a point P on a level ground , the angle of elevation to the top of the tower is 30° . If the tower is 100m high , the distance of point P from the foot of the tower is ( Take √3 = 1.73)

A. 149 m

B. 156 m

C. 173 m

D. 188 m

Question 68

If the elevation of the Sun changes from 30° to 60° , then the difference between the lengths of shadows of a pole 15 m high, is

A. 7.5 m

B. 15 m

C. 10√3 m

D. 5√3 m

Question 69

The angle of elevation of the top of a tower at a distance of 25 m from its foot is 60 deg. The approximate height of the tower is

A. 20.3 m

B. 15.3 m

C. 36.3 m

D. 43.3 m

Question 70

From the top of a platform 5 m high, the angle of elevation of a tower was 30 deg. If the tower was 45 m high, how far away from the tower was the platform positioned?

A. 15√3 m

B. 40√3 m

C. 45√3 m

D. 40 m

Question 71

The angle of elevation of an aeroplane from a point on the ground is 60 deg. After flying for 30 seconds, the angle of elevation changes to 30 deg. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?

A. 50√3

B. 100√3

C. 200√3

D. 300√3

Question 72

A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60 to 45 deg. What is the height (in metres) of the lighthouse?

A. 240√3

B. 480[(√3) – 1]

C. 360√3

D. 280√2

Question 73

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

A. 4 m

B. 7 m

C. 9 m

D. 6 m

Question 74

The upper part of a tree broken over by the wind make an angle of 60 deg with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?

A. 84.14

B. 93.3

C. 98.25

D. 120.24

Question 75

From a point P on a level ground, the angle of elevation of the top tower is 30 degree. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A. 149 m

B. 150 m

C. 173 m

D. 200 m