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Answer :

Explanation

If the height of an object h varies directly with the length of its shadow l then both quantities are related by an expression like this one:

[tex]h=k\cdot l[/tex]

Where k is a number. We are told that a 6 ft tall person has a 15 ft long shadow. This means that for h=6 we have l=15. Then we can construct an equation for k:

[tex]6=15k[/tex]

We can divide both sides by 15:

[tex]\begin{gathered} \frac{6}{15}=\frac{15k}{15} \\ k=\frac{2}{5}=0.4 \end{gathered}[/tex]

So the relation between height and the length of the shadow is:

[tex]h=0.4l[/tex]

Then if the tree is 20 ft tall we get:

[tex]20=0.4l[/tex]

We can divide both sides by 0.4:

[tex]\begin{gathered} \frac{20}{0.4}=\frac{0.4l}{0.4} \\ l=50 \end{gathered}[/tex]Answer

Then the answer is 50 ft.

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