Heights & Distances
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Quantitative Aptitude - Heights & Distances
Learn the trigonometric approach to solving problems involving the height of objects and distances using angles of elevation and depression.
1. Basic Concepts
- Angle of Elevation: Angle from horizontal upward to an object.
- Angle of Depression: Angle from horizontal downward to an object.
- Right triangle is formed with object, observer, and ground/horizontal.
2. Key Trigonometric Ratios
- \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \)
- \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \)
- \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \)
3. Common Values
- \( \tan 30° = \frac{1}{\sqrt{3}}, \tan 45° = 1, \tan 60° = \sqrt{3} \)
4. Example
Angle of elevation to top of tower = 45°, distance from base = 50m
- \( \tan 45° = h/50 → h = 50m \)
5. Strategy & Tips
- Draw triangle with correct angle and distances.
- Use appropriate trigonometric function depending on known values.
Summary: Most height & distance problems reduce to applying right-angle trigonometry. Diagrams help avoid confusion.
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