Shadow Based Distance
Shadow Based Distance problems use the principle of similar triangles to find heights or shadow lengths. When light rays from a source (sun or lamp) create shadows, the ratio of height to shadow length is constant for all objects at the same time.
What You'll Learn
Introduction to Shadow Based Distance
Shadow Based Distance problems use the principle of similar triangles to find heights or shadow lengths. When light rays from a source (sun or lamp) create shadows, the ratio of height to shadow length is constant for all objects at the same time.
Prerequisites
How to Solve Shadow Based Distance Problems
Step 1: Identify the known height and shadow length
Step 2: Set up proportion: Height₁ / Shadow₁ = Height₂ / Shadow₂
Step 3: Substitute known values
Step 4: Cross-multiply to solve for unknown
Step 5: Calculate the result
Step 6: Answer with appropriate units
Example Problem
Example: A 1.5 m tall person casts a 2 m shadow. A building casts a 10 m shadow at the same time. Find building height. Solution: Step 1: Person: H₁ = 1.5 m, S₁ = 2 m Step 2: Building: H₂ = ?, S₂ = 10 m Step 3: Proportion: 1.5/2 = H₂/10 Step 4: H₂ = (1.5 × 10)/2 = 15/2 = 7.5 m Answer: 7.5 m
Pro Tips & Tricks
- Height/Shadow = constant for same time
- If two shadows are given, use H₁/S₁ = H₂/S₂
- For lamp post problems, consider the distance from the lamp
- Similar triangles apply when light source is at a distance (sun)
- For point light sources, use different geometry
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Shadow Based Distance. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Shadow Based Distance is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Shadow Based Distance?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: