# The length of man’s shadow.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.6, Problem 51E
To determine

## To find: The length of man’s shadow.

Expert Solution

The length of man’s shadow is 5 m.

### Explanation of Solution

Given:

The height of lamppost is 6 m and the height of man is 2 m.

The distance between the lamppost and man is 10 m.

Calculation:

Let the length of man’s shadow be x. For a pair of similar triangles the ratios of corresponding sides are equal.

Tabulate the given information into the language of algebra.

 In words In Algebra Length of shadow x Base of large triangle 10+x Ratio of height to base in large triangle 610+x Ratio of height to base in small triangle 2x

Model the equation for the above information.

(Ratioofheighttobaseinlargetriangle)=(Ratioofheighttobaseinsmalltriangle)610+x=2x

Simplify the above equation for x,

6x=2(10+x)6x=20+2x4x=20x=5

Thus, the length of man’s shadow is 5 m.

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