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Home Continuous Functions How to Set Up a Problem Examples Example 2: Length of a Shadow (Two Variables)
 
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Example 2: Length of a Shadow (Two Variables)

A six-foot man stands near a ten-foot lamppost. Find the length of his shadow as a function of his distance from the lamppost.

03_continuous_functions-6.gif

Figure 3.1.2

Step 1

Draw a diagram and label all the quantities involved. In Figure 3.1.2, we let

x = man's distance from lamppost,
s = length of his shadow.

Step 2

Write the known information as a system of formulas. By similar triangles we have

03_continuous_functions-7.gif, x ≥ 0.

The inequality x ≥ 0 arises because the distance cannot be negative.

Step 3

Solve for s as a function of x.

10s = 6s + 6x,
4s = 6x,
s = 3/2 x.

INTERPRET THE SOLUTION

s = 3/2x,     x ≥ 0.

The domain of the function is [0, ∞). The length of the shadow is 3/2 times the distance from the lamppost. In this problem, x is the independent variable and s depends on x.
Home Continuous Functions How to Set Up a Problem Examples Example 2: Length of a Shadow (Two Variables)

Last Update: 2006-11-15