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SSC GD Constable Heights & Distances

Study Material — 10 PYQs (2021–2021) · Concept Notes · Shortcuts

SSC GD Constable Heights & Distances is a frequently tested subtopic — 10 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.

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2021–2021

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Previous Year Questions

SSC GD Constable Heights & Distances — Past Exam Questions

10 questions from actual SSC GD Constable papers · all shown free · click option to reveal solution

Exam Q 12021Previous Year Pattern

A ladder leans against a wall such that it makes an angle of 30° with the ground. If the ladder is 10 metres long, what is the height at which the ladder touches the wall?

Exam Q 22021Previous Year Pattern

An observer on the ground sees the top of a tree at an angle of elevation of 60°. If the observer is 15 metres away from the base of the tree, what is the height of the tree? (Use √3 ≈ 1.73)

Exam Q 32021Previous Year Pattern

From a point on the ground, the angle of elevation to the top of a 20-metre tall building is 45°. How far is the point from the base of the building?

Exam Q 42021Previous Year Pattern

A man standing 30 metres away from the base of a tower observes the angle of elevation to the top of the tower as 60°. Find the height of the tower.

Exam Q 52021Previous Year Pattern

From the top of a 48-metre tall building, the angle of depression to a point on the ground is 30°. What is the horizontal distance from the building to that point?

Exam Q 62021Previous Year Pattern

Two buildings are 60 m apart. From the top of the first building (height 30 m), the angle of elevation to the top of the second building is 45°. Find the height of the second building.

Exam Q 72021Previous Year Pattern

A man standing 40 m away from the base of a tower observes the angle of elevation to the top of the tower as 60°. Find the height of the tower (in metres). [Use √3 ≈ 1.732]

Exam Q 82021Previous Year Pattern

From the top of a cliff 100 m high, the angle of depression to a boat in the sea is 30°. How far is the boat from the base of the cliff? [Use √3 ≈ 1.732]

Exam Q 92021Previous Year Pattern

A person standing on the ground observes the angle of elevation to the top of a tree as 45°. After walking 10 m towards the tree, the angle of elevation becomes 60°. Find the height of the tree. [Use √3 ≈ 1.732]

Exam Q 102021Previous Year Pattern

A ladder leans against a vertical wall. The foot of the ladder is 6 m from the wall, and the ladder makes an angle of 60° with the ground. A person climbs to a point on the ladder where the angle of elevation from the ground (at the foot of the ladder) to that point is 45°. How far up the wall is this point?

Concept Notes

Heights & Distances— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

When you look up at a tall building, the angle your line of sight makes with the horizontal ground is called the angle of elevation. When you look down from a height, it's called the angle of depression. These angles help us calculate heights and distances we cannot measure directly

KEY RULES

The angle of elevation from point A to point B equals the angle of depression from point B to point A. Always draw a right triangle and identify the opposite side, adjacent side, and hypotenuse clearly. The horizontal distance remains constant in most problems.

2.Formula Block

Memorise — at least one formula appears in every paper

• tan θ = Height/Base (most used)

• sin θ = Height/Hypotenuse

• cos θ = Base/Hypotenuse

• When angle changes from α to β: New height = Base × (tan β - tan α) + Original height

3.Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL consistently asks 1-2 questions on this topic. Common scenarios include: tower/building height from given distance, finding distance when height is known, problems involving two angles of elevation, lighthouse/ship problems, and ladder-wall problems.

4.Shortcuts

Use these to save 30–60 seconds per question

- ANGLE CHANGE METHOD: When moving closer or farther from an object, use the formula: h = d₁ × tan α = d₂ × tan β, where h is height, d is distance, and α, β are angles. This eliminates the need to calculate height separately.

5.Worked Example

Solve this step-by-step before moving on

1

Step 1

Draw diagram with tower height = h, man's height = 1.8m, horizontal distance = 150m

2

Step 2

Effective height to calculate = h - 1.8m (since man has height)

3

Step 3

tan 30° = (h - 1.8)/150

4

Step 4

1/√3 = (h - 1.8)/150

5

Step 5

h - 1.8 = 150/√3 = 150/1.732 = 86.6m

6

Step 6

h = 86.6 + 1.8 = 88.4m WORKED EXAMPLE 2: From a point on ground, a tree top's angle of elevation is 45°. Moving 20m closer, the angle becomes 60°. Find tree height.

1

Step 1

Let tree height = h, original distance = d

2

Step 2

From original position: tan 45° = h/d, so h = d

3

Step 3

From new position: tan 60° = h/(d-20)

4

Step 4

√3 = h/(d-20) = d/(d-20) [since h = d]

5

Step 5

√3(d-20) = d

6

Step 6

1.732d - 34.64 = d

7

Step 7

0.732d = 34.64, so d = 47.32m

8

Step 8

Tree height h = d = 47.32m

6.Exam Traps

Common mistakes students make — avoid these

#1: Students forget to account for the observer's height. When a person observes something, always subtract the person's height from the total height calculated. Many students calculate the total vertical distance but forget the observer is not on the ground level. ADDITIONAL SHORTCUTS: For 30-60-90 triangles, use ratio 1:√3:2.

For 45-45-90 triangles, use ratio 1:1:√2. When angle of elevation doubles, use the identity tan(2θ) = 2tan(θ)/(1-tan²θ). Remember that complementary angles have reciprocal trigonometric ratios.

Key Points to Remember

Angle of elevation = angle looking up; angle of depression = angle looking down
tan θ = Height/Base is the most frequently used formula in height-distance problems
Always subtract observer's height from total calculated height
Angle of elevation from A to B = Angle of depression from B to A
For 30° angle: tan 30° = 1/√3 = 0.577
For 45° angle: tan 45° = 1
For 60° angle: tan 60° = √3 = 1.732
In two-angle problems, use h = d₁ × tan α = d₂ × tan β shortcut
Draw clear diagrams marking height, base, and angles before solving
Horizontal distance remains same; only vertical measurements change with angle

Exam-Specific Tips

tan 30° = 1/√3 = 0.5774 (exact value)
tan 45° = 1 (exact value)
tan 60° = √3 = 1.732 (exact value)
sin 30° = 1/2 = 0.5
cos 30° = √3/2 = 0.866
sin 45° = cos 45° = 1/√2 = 0.707
sin 60° = √3/2 = 0.866
cos 60° = 1/2 = 0.5

Practice MCQs

Heights & Distances — Practice Questions

2graded MCQs · easy to hard · full solution & trap analysis

All MCQs →

Practice 1hard

A vertical pole of height 12 m casts a shadow of length 12√3 m on level ground. At the same time, a building casts a shadow of 36 m. If the angle of elevation to the top of the building from the tip of its shadow is θ, find cot(θ).

Practice 2hard

From the top of a cliff 80 m high, the angles of depression to two boats on the water are 30° and 60° respectively. Both boats are on the same side of the cliff and in line with the point directly below the observer. Find the distance between the boats.

60-Second Revision — Heights & Distances

Remember: Always draw diagram first and mark given angles and distances clearly
Formula: tan θ = Height/Base is the primary formula for 90% of problems
Trap: Don't forget to subtract observer's height from calculated total height
Shortcut: Use tan 30° = 0.577, tan 45° = 1, tan 60° = 1.732 for quick calculations
Pattern: Two-angle problems use h = d₁ × tan α = d₂ × tan β relationship
Check: Angle of elevation and depression are always measured from horizontal line
Quick tip: 30-60-90 triangle sides are in ratio 1:√3:2

←Basic Trig Ratios Trig Identities→

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