# The height of taller tree. ### 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 52E
To determine

## To find: The height of taller tree.

Expert Solution

The height of taller tree is 95 ft.

### Explanation of Solution

Given:

The distance between taller tree and smaller tree is 125 ft.

The height of man is 5ft and the height of smaller tree is 20 ft.

Distance between man and smaller tree is 25 ft.

Calculation:

Let the height of taller tree 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 Height of taller tree x Base of large triangle 25+125 Ratio of height to base in large triangle x−525+125 Ratio of height to base in small triangle 20−525

Model the equation for the above information.

(Ratioofheighttobaseinlargetriangle)=(Ratioofheighttobaseinsmalltriangle)x525+125=20525

Simplify the above equation for x,

25(x5)=15×15025x125=225025x=2375x=95

Thus, the height of taller tree is 95 ft.

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