   Chapter 5.2, Problem 31E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercise 29 to 32, use the fact that triangles are similar.While admiring a rather tall tree, Fred notes that the shadow of his 6 -ft frame has a length of 3 paces. On the level ground, he walks off the complete shadow of the tree in 37 paces. How tall is the tree?

To determine

To calculate:

The height of the tree.

Explanation

Given:

While admiring a rather tall tree, Fred notes that the shadow of his 6ft frame has a length of 3 paces. On the level ground, he walks off the complete shadow of the tree in 37 paces.

Definition Used:

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

Calculation:

Consider the following graph.

Here, AB¯ represents the height of the tree, DB¯ represents the shadow of the tree, CD¯ represents the height of the Fred, and DE¯ represents the shadow of the Fred.

It is given that the shadow of the complete tree is BE=37ft.

The height of Fred is CD=6ft.

The shadow of the Fred is DE=3panes

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