Heights & Distances
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Cheat Sheets
Study MaterialHeights and Distances Cheat Sheet
Heights and Distances is one of the most important trigonometry-based topics in Quantitative Aptitude and is frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, and other competitive examinations.
This cheat sheet helps candidates understand trigonometric ratios, angle of elevation and depression, shadow problems, tower and building height calculations, and shortcut techniques for solving heights and distances problems quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Heights and Distances for competitive exams:
Basic Trigonometric Ratios
- sin θ
- cos θ
- tan θ
- cot, sec & cosec
Standard Angle Values
- 0°
- 30°
- 45°
- 60°
- 90°
Angle of Elevation & Depression
- Line of Sight
- Above Horizontal
- Below Horizontal
- Observer Problems
Height & Distance Problems
Finding heights of towers, poles, buildings, and distances using trigonometry.
Shadow & Sun Problems
- Length of Shadow
- Sun Altitude
- Height Calculations
- Time Based Problems
Multiple Object Problems
- Two Towers
- Buildings & Poles
- Cloud & Balloon Problems
- Moving Observer Problems
Important Concepts
- Pythagoras Theorem
- Trigonometric Identities
- Approximation Methods
- Distance Calculations
Shortcut Tricks
Fast solving methods, trigonometry shortcuts, and exam-oriented geometry techniques.
Topics Covered
| Topic | Description |
|---|---|
| Trigonometric Ratios | sin, cos, tan, cot, sec, cosec formulas |
| Standard Angles | Values for 0°, 30°, 45°, 60°, 90° |
| Angle of Elevation | Line of sight above horizontal |
| Angle of Depression | Line of sight below horizontal |
| Height of Tower | Calculating height using trigonometry |
| Distance Problems | Finding distance from observation point |
| Shadow Problems | Height and shadow relation |
| Cloud & Balloon Problems | Height estimation problems |
| Multiple Object Problems | Problems involving towers and buildings |
| Moving Observer Problems | Approaching or moving away concepts |
| Pythagoras Theorem | Right-angle triangle calculations |
| Trigonometric Identities | Important trigonometric relations |
| Approximation Techniques | Fast estimation methods |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Trigonometry Concepts
↓
Improve Geometrical Thinking
↓
Apply Shortcut Techniques
↓
Solve Height & Distance Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Examples
Example 1:
Find the height of a tower if the angle of elevation is 45° and the distance from the tower is 20 m.
tan 45° = Height / Distance
1 = Height / 20
Height = 20 m
Example 2:
A pole casts a shadow of 10 m when the angle of elevation of the sun is 30°. Find the height of the pole.
tan 30° = Height / 10
1/√3 = Height / 10
Height = 10/√3 m
Example 3:
Find the distance of a building from a point if its height is 15 m and angle of elevation is 60°.
tan 60° = 15 / Distance
√3 = 15 / Distance
Distance = 15/√3
= 5√3 m
Example 4:
Find the value of sin 30°.
sin 30° = 1/2
Example 5:
An observer moves 10 m closer to a tower and angle of elevation changes from 30° to 60°. Find the height of tower.
Using trigonometric equations:
Height = 5√3 m
Final Takeaway
This Heights and Distances Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of trigonometric ratios, angle of elevation and depression problems, shadow concepts, and shortcut techniques can significantly improve speed, accuracy, and geometrical problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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