Question

George, who is 6.25
-feet tall, needs to know the height of a tree that he is going to cut down. He notices that he casts a 10
-foot shadow when the tree casts a 28
-foot shadow. The height of the tree is blankfeet tall. Enter only the number.

Answer 1

To find the height of the tree, we can use the concept of similar triangles. Since both George and the tree cast shadows of different lengths, we can set up a proportion based on their heights and the lengths of their shadows.

Let \( h \) be the height of the tree in feet. We have:

\[
\frac{\text{Height of George}}{\text{Shadow of George}} = \frac{\text{Height of Tree}}{\text{Shadow of Tree}}
\]

Plugging in the values we have:

\[
\frac{6.25}{10} = \frac{h}{28}
\]

To solve for \( h \), cross-multiply:

\[
6.25 \cdot 28 = 10 \cdot h
\]

Calculating \( 6.25 \cdot 28 \):

\[
6.25 \cdot 28 = 175
\]

Now we have:

\[
175 = 10h
\]

Dividing both sides by 10:

\[
h = \frac{175}{10} = 17.5
\]

Thus, the height of the tree is **17.5** feet tall.