Question

Suppose that you are 5 feet 3 inches tall and cast a shadow 10 feet 6 inches long. If you are standing nextto a tree that casts a shadow that is 52 feet long, about how tall is the tree?

Answer 1

Let be "x" the height in feet of the tree.

First, we need to make the conversion from inches to feet. Since:

`1\text{ ft=12 in}`

We have:

`\begin{gathered} (3\text{ in)(}\frac{1\text{ ft}}{12\text{ in}})=0.25\text{ ft} \\ \\ (6\text{ in)(}\frac{1\text{ ft}}{12\text{ in}})=0.5\text{ ft} \end{gathered}`

Then your height is:

`5\text{ ft+0.25 ft= 5.25 ft}`

And your shadow is:

`10\text{ f+ 0.5 ft=10.5 ft}`

Knowing that, we can set up the following proportion:

`(5.25)/(10.5)=(x)/(52)`

Solving for "x", we get:

`\begin{gathered} ((5.25)/(10.5))(52)=x \\ x=\text{ 26} \end{gathered}`

Therefore, the height of the tree is about 26 feet.