Heights & Distances
View Questions of Heights & Distances
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.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations
Other Subjects
- Prestressed Concrete
- Fluid Mechanics
- Geotechnical Engineering
- Ground Improvement Techniques
- Groundwater Engineering
- Highway Engineering
- Hydraulics and Hydraulic Machines
- Hydrology
- Irrigation Engineering
- Open Channel Flow
- Pavement Design
- Estimation, Costing and Valuation
- Railway Engineering
- Soil Mechanics
- Strength of Materials
- Structural Analysis
- Surveying
- Traffic Engineering
- Transportation Engineering
- Wastewater Treatment
- Water Supply and Sanitation
- Contracts and Specifications
- Reasoning
- Engineering Mathematics
- Air Pollution and Control
- Bridge Engineering
- Building Materials and Construction
- Concrete Technology
- Construction Equipment
- Construction Planning and Management
- Quantitative Aptitude
- Dam Engineering
- Design of RCC Structures
- Design of Steel Structures
- Drainage Engineering
- Earthquake Engineering
- Engineering Geology
- Engineering Graphics
- Engineering Mechanics
- Environmental Engineering
- General Awareness / General Knowledge (GK)