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.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

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

Similar triangles concept Ratio and proportion Height and shadow relationship Basic geometry
Why This Matters: Shadow Based Distance problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test application of similar triangles in real-world contexts.

How to Solve Shadow Based Distance Problems

1

Step 1: Identify the known height and shadow length

2

Step 2: Set up proportion: Height₁ / Shadow₁ = Height₂ / Shadow₂

3

Step 3: Substitute known values

4

Step 4: Cross-multiply to solve for unknown

5

Step 5: Calculate the result

6

Step 6: Answer with appropriate units

Pro Strategy: At the same time, the sun's angle is constant, so the ratio of height to shadow length is constant for all objects. Use cross-multiplication to find the unknown.

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

H₂ = (H₁ × S₂)/S₁
S₂ = (S₁ × H₂)/H₁
If shadow of a vertical pole is given, height is proportional to shadow

Common Mistakes to Avoid

Using inverse proportion incorrectly
Forgetting that the ratio is height to shadow, not shadow to height
Not ensuring the time is the same

Exam Importance

Shadow Based Distance is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Shadow Based Distance?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now