Question

A 24-foot-tall tree casts a shadow that is 10 feet long. What is the distance from the top of the tree to the top of its shadow? Apply a Pythagorean triple to solve this problem. (1 point)
feet

Answer 1

To find the distance from the top of the tree to the top of its shadow, we can visualize this as a right triangle. The height of the tree is one leg of the triangle, and the length of the shadow is the other leg. The distance from the top of the tree to the top of the shadow is the hypotenuse of the right triangle.

Given:
- Height of the tree (a) = 24 feet
- Length of the shadow (b) = 10 feet

We can use the Pythagorean theorem, which states:

\[
c^2 = a^2 + b^2
\]

where \(c\) is the length of the hypotenuse.

Substituting in the values:

\[
c^2 = 24^2 + 10^2
\]
\[
c^2 = 576 + 100
\]
\[
c^2 = 676
\]
\[
c = \sqrt{676}
\]
\[
c = 26
\]

Thus, the distance from the top of the tree to the top of its shadow is **26 feet**.