Question

A tree of unknown height cast a shadow that is 20 ft long. If a person is 5 feet seven cast a shadow that is 5 ft long then how tall is the tree in feet? Round to the nearest integer

Answer 1

This is a problem of similar triangles, then let's make a sketch of the situation:

Then, those triangles are similar, then if we call x the height of the tree, the theorem of similar triangles states:

`(x)/(5ft7in)=(20ft)/(5ft)`

First let's convert 5ft7in to feet:

`\begin{gathered} (1ft)/(12in)=(x)/(7in) \\ x=(7)/(12)=0.58ft \\ \text{Then 5ft7in=5.58ft} \end{gathered}`

Now, let's solve for x:

`\begin{gathered} (x)/(5.58ft)=(20ft)/(5ft) \\ x=(20*5.58)/(5) \\ x=(111.7)/(5) \\ x=22.33\approx22ft \end{gathered}`

Then the height of the tree is 22 ft