A ladder 12 m long leans against a vertical wall and its top touches the wall 6 m above the ground. What angle does the ladder make with the ground?
Correct answer A. 30°
Topic / 37 questions
Height and Distance MCQs
Height and Distance MCQs use basic trigonometry to find heights of towers, lengths of shadows and distances between objects from angles of elevation and depression. They appear in NTS, ECAT, SSC and other aptitude tests. Each question has an instant answer, so you can check your use of tangent and the standard angle values.
- Numbers 104
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- Age Questions 95
- Profit and Loss 82
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- Time and Work 73
- Alligation or Mixture 73
- Fraction and Decimal 72
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- Area 64
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- Equations and Inequalities 64
- Time and Distance 64
- Simplification 60
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- Problems on Numbers 47
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- Odd Man Out and Series 43
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- Clock 39
- Races and Games 38
- Height and Distance 37
- True Discount 36
- Stocks and Shares 34
- Boats and Streams 34
- Banker's Discount 32
- Counting 32
- Logarithm 30
- Problems on H.C.F and L.C.M 30
- Calendar 30
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- Word Problems 25
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From the top of a building 20 m high, the angle of elevation of the top of a taller tower is 45° and the angle of depression of the foot of the tower is 30°. Taking √3 = 1.732, what is the height of the tower?
Correct answer B. 54.64 m
A man whose eyes are 1.8 m above the ground stands 28.2 m from the foot of a vertical tower. The angle of elevation of the top of the tower from his eyes is 45°. What is the height of the tower?
Correct answer C. 30 m
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The shadow of a vertical tower on level ground is 40 m longer when the sun’s elevation is 30° than when it is 60°. Taking √3 = 1.732, what is the height of the tower?
Correct answer B. 34.64 m
A flagstaff stands on top of a building 25 m high. From a point on the ground, the angle of elevation of the top of the building is 45° and that of the top of the flagstaff is 60°. Taking √3 = 1.732, what is the length of the flagstaff?
Correct answer B. 18.30 m
A storm breaks a vertical tree so that its top touches the ground 14 m from the foot, with the broken part making an angle of 30° with the ground. Taking √3 = 1.732, what was the original height of the tree?
Correct answer C. 24.25 m
An aeroplane flies horizontally at a height of 1500 m. From a point on the ground, its angle of elevation changes from 60° to 30° in 10 seconds. Taking √3 = 1.732, what is the speed of the aeroplane in km/h?
Correct answer D. 623.52 km/h
A vertical tower is 30 m high. A point on level ground is 30√3 m from its foot. What is the angle of elevation of the top of the tower from that point?
Correct answer A. 30°
A man on top of a tower watches a car approaching the tower at a uniform speed. The angle of depression of the car changes from 30° to 60° in 12 minutes. How much more time will the car take to reach the foot of the tower?
Correct answer A. 6 minutes
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Two vertical poles of equal height stand on opposite sides of a straight road 120 m wide. From a point on the road between them, the angles of elevation of their tops are 60° and 30°. Taking √3 = 1.732, what is the height of each pole?
Correct answer B. 51.96 m
A lighthouse 80 m high stands on the shore. Two ships are on opposite sides of it, in line with its foot, and the angles of depression from the top of the lighthouse to the ships are 45° and 60°. Taking √3 = 1.732, what is the distance between the ships?
Correct answer B. 126.19 m
At a certain time of day the angle of elevation of the sun is 30°. A building on level ground casts a shadow 45 m long at that time. Taking √3 = 1.732, what is the height of the building?
Correct answer C. 25.98 m
From two points on level ground on the same side of a tower and in line with its foot, the angles of elevation of the top are 45° and 30°. The two points are 50 m apart. Taking √3 = 1.732, what is the height of the tower?
Correct answer A. 68.30 m
From a window 15 m above the ground, the angle of elevation of the top of a building across the street is 30° and the angle of depression of its foot is 45°. Taking √3 = 1.732, what is the height of the building?
Correct answer B. 23.66 m
A statue 7.32 m tall stands on a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and that of the top of the pedestal is 45°. Taking √3 = 1.732, what is the height of the pedestal?
Correct answer C. 10.00 m
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At a certain moment, the shadow of a vertical pole on level ground is exactly equal to the height of the pole. What is the angle of elevation of the sun?
Correct answer D. 45°
A balloon rises vertically from a point on level ground. An observer 300 m from that point sees the angle of elevation of the balloon change from 30° to 60°. Taking √3 = 1.732, how far has the balloon risen in that time?
Correct answer D. 346.40 m
From the top of a tower 60 m high, the angles of depression of the top and the foot of a shorter pillar standing on the same level ground are 30° and 60° respectively. What is the height of the pillar?
Correct answer D. 40 m
A point on level ground is 40 m from the foot of a vertical tower, and the angle of elevation of the top of the tower from this point is 60°. What is the straight-line distance from the point to the top of the tower?
Correct answer D. 80 m
From the top of a cliff 60 m high, the angles of depression of two boats on the same side of the cliff and in line with its foot are 45° and 60°. Taking √3 = 1.732, what is the distance between the boats?
Correct answer B. 25.36 m
About Height and Distance MCQs
These problems are applications of right-angled triangle trigonometry. In this set you will find the angle of the sun from the length of a tree's shadow, the distance of an observer from a tower of known height, and the distance between two ships seen from a lighthouse. A ladder question uses the cosine of the angle with the ground, and one item tests logarithms. Remembering that tan 30 degrees is 1 over root 3, tan 45 degrees is 1 and tan 60 degrees is root 3 solves most questions quickly. Always draw a labelled sketch first.
Exams that include Height and Distance MCQs
Pakistan
- NTS
- ECAT
- ISSB
- FPSC
India
- SSC CGL
- SSC CHSL
- NDA
Bangladesh
- Engineering admission (BUET)
- Government job tests
Frequently asked questions
What is an angle of elevation?
An angle of elevation is the angle between the horizontal line from an observer's eye and the line of sight to an object above them, such as the top of a tower. An angle of depression is the matching angle when looking down at an object below the horizontal.
A tower is 100 m high and its top is seen at 30 degrees elevation. How far away is the observer?
Use tan 30 degrees equals height divided by distance. Since tan 30 degrees is 1 over root 3, the distance equals 100 times root 3, which is about 173.2 metres. Drawing the right triangle first makes the choice of ratio clear.
Last reviewed October 2026