Height and Distance

Quantitative Aptitude

Page 1 of 3 • 30 total questions

Quantitative Aptitude • Height and Distance
5 marksView Details

From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are found to be 30° and 60° respectively. If the tower and the cliff are on the same side of a river, what is the width of the river?

A

200/√3 m

B

200√3 m

C

400/√3 m

D

100√3 m

Quantitative Aptitude • Height and Distance
5 marksView Details

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retreats 40 m from the bank, he finds the angle to be 30°. What is the breadth of the river and the height of the tree?

A

Breadth = 20 m, Height = 20√3 m

B

Breadth = 40 m, Height = 40√3 m

C

Breadth = 30 m, Height = 30√3 m

D

Breadth = 10 m, Height = 10√3 m

Quantitative Aptitude • Height and Distance
5 marksView Details

A man on the top of a vertical observation tower observes a car moving at uniform speed towards the tower. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how much more time will it take for the car to reach the tower?

A

6(√3 + 1) minutes

B

12 minutes

C

6(√3 - 1) minutes

D

18 minutes

Quantitative Aptitude • Height and Distance
5 marksView Details

The angle of elevation of the top of an unfinished tower at a point 120 m from its base is 30°. If the angle of elevation of the top of the finished tower at the same point is 60°, what is the height by which the tower was raised?

A

80√3 m

B

120√3 m

C

160 m

D

240 m

Quantitative Aptitude • Height and Distance
5 marksView Details

A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. What should be the height of another tower on the opposite side of the same point, if the angles of elevation of the tops of the two towers from that point are complementary?

A

20/√3 m

B

20√3 m

C

40/√3 m

D

60 m

Quantitative Aptitude • Height and Distance
5 marksView Details

From the top of a cliff 150√3 m high, the angles of depression of two boats which are due south of the observer are 60° and 30°. What is the distance between the two boats?

A

300 m

B

150√3 m

C

200√3 m

D

450 m

Quantitative Aptitude • Height and Distance
5 marksView Details

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation of the bottom and top of the flagstaff are α and β respectively. What is the height of the tower?

A

h tan α/(tan β - tan α)

B

h tan β/(tan β - tan α)

C

h(tan β - tan α)/tan α

D

h tan α tan β/(tan β - tan α)

Quantitative Aptitude • Height and Distance
5 marksView Details

A man observes that when he moves 10 m towards a tower, the angle of elevation changes from 30° to 45°. If he moves another 10 m in the same direction, what will be the new angle of elevation?

A

tan⁻¹(√3/2)

B

60°

C

tan⁻¹(2/√3)

D

30°

Quantitative Aptitude • Height and Distance
5 marksView Details

The angle of elevation of a cloud from a point h meters above a lake is α and the angle of depression of its reflection is β. What is the height of the cloud above the lake?

A

h(tan β + tan α)/(tan β - tan α)

B

h(tan α + tan β)/(tan α - tan β)

C

h tan α/tan β

D

h(tan β - tan α)/(tan β + tan α)

Quantitative Aptitude • Height and Distance
5 marksView Details

Two vertical poles of heights 20 m and 80 m stand apart on a horizontal plane. The line joining the top of the poles makes an angle of 45° with the horizontal. What is the distance between the two poles?

A

60 m

B

40 m

C

80 m

D

100 m

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