Question

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)
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Answer 1

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

Given:
- Height of the tree (one leg) = 24 feet
- Length of the shadow (the other leg) = 10 feet

We will use the Pythagorean theorem:

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

where:
- \(a\) = height of the tree = 24 feet
- \(b\) = length of the shadow = 10 feet
- \(c\) = distance from the top of the tree to the top of the shadow (hypotenuse)

Plugging in the values:

\[
24^2 + 10^2 = c^2
\]

Calculating \(24^2\) and \(10^2\):

\[
576 + 100 = c^2
\]

Adding these together:

\[
676 = c^2
\]

Now, take the square root of both sides to find \(c\):

\[
c = \sqrt{676} = 26
\]

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