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Chapter 8: Q. 8.160 (page 995)

A pine tree casts a shadow of 80feet next to a 30-foot tall building which casts a 40 feet shadow. How tall is the
pine tree?

Short Answer

Expert verified

The height of the pine tree is 60feet

Step by step solution

01

Step 1. Given Information

Height of the pine tree shadow=80

Height of a building=30

Height of the shadow of building=40

02

Step 2. Read the problem and draw a figure.

Read the problem and draw a figure.

03

Step 3. Use similar triangles to write an equation.

The small triangle is similar to the large triangle.

h80=3040

04

Step 4. Solve the proportion.

Solve the proportion and simplify.

h80=3040h=3040脳80=60

The height of the tree is 60feet

05

Step 5. Check the answer

Building's height is less than its shadow's length so it makes
sense that the tree's height is less than the length of its shadow.

6080=304034=34

So the equation is true.

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