Question

A tree cast a shadow 10 ft long. A Boy standing next to the tree cast a shadow 2.5 ft. long. The triangle show for the tree and its shadow is similar to the triangle shadow for the boy and his shadow. If the boy is 5 ft. tall how tall is the tree?

Answer 1

Hrmm I'm not sure but for some reason i keep on getting \(\ 20\) as my answer.

Answer 2

Btw you have options?

Answer 3

how do you get to the answer

Answer 4

Diagram:

Because the triangles formed by the boy/his shadow and the tree/its shadow, the corresponding lengths/heights are proportional. This means
\[\frac{\text{height of tree}}{\text{height of boy}}=\frac{\text{length of tree's shadow}}{\text{length of boy's shadow}}\iff\frac{x}{5}=\frac{10}{2.5}\]