Question

Draw and solve the following problem: In the early afternoon, a tree casts a shadow that is 2 feet long. A 4.2-foot-tall boy standing next to the tree casts a shadow that is 0.7 feet long. How tall is the tree?

Answer 1

To solve the problem, we can use the concept of similar triangles. The height of the tree and its shadow, as well as the height of the boy and his shadow, create two similar triangles.

Let:
- \( h \) be the height of the tree (in feet).
- The height of the boy is 4.2 feet.
- The length of the tree's shadow is 2 feet.
- The length of the boy's shadow is 0.7 feet.

Since the triangles are similar, we can set up a proportion:

\[
\frac{\text{Height of the boy}}{\text{Shadow of the boy}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]

Substituting the known values into the proportion:

\[
\frac{4.2}{0.7} = \frac{h}{2}
\]

Now, we simplify the left side of the equation:

\[
\frac{4.2}{0.7} = 6
\]

So we have:

\[
6 = \frac{h}{2}
\]

To solve for \( h \), we can multiply both sides by 2:

\[
h = 6 \times 2
\]

\[
h = 12
\]

Thus, the height of the tree is **12 feet**.