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

Question

contestada

Respuesta :

WhisperW678380 WhisperW678380 · Answer 1 · 2022-10-28T22:26:58+02:00

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:

[tex]\frac{x}{5ft7in}=\frac{20ft}{5ft}[/tex]

First let's convert 5ft7in to feet:

[tex]\begin{gathered} \frac{1ft}{12in}=\frac{x}{7in} \\ x=\frac{7}{12}=0.58ft \\ \text{Then 5ft7in=5.58ft} \end{gathered}[/tex]

Now, let's solve for x:

[tex]\begin{gathered} \frac{x}{5.58ft}=\frac{20ft}{5ft} \\ x=\frac{20\times5.58}{5} \\ x=\frac{111.7}{5} \\ x=22.33\approx22ft \end{gathered}[/tex]

Then the height of the tree is 22 ft