The height of the tree and its shadow, and the height of the person and its shadow, at the same time of the day, form two similar right triangles:
Since both triangles are similar, then the corresponding sides are at the same ratio so that:
[tex]\begin{gathered} \frac{\text{height tree}}{\text{height person}}=\frac{shadow\text{ tree}}{shadow\text{ person}} \\ \frac{x}{5}=\frac{24}{8} \end{gathered}[/tex]From this expression, you can determine the height of the tree, just multiply both sides of the equal sign by 5:
[tex]\begin{gathered} 5\cdot\frac{x}{5}=5\cdot\frac{24}{8} \\ x=5\cdot3 \\ x=15ft \end{gathered}[/tex]The height of the tree is 15 feet.
