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)

Answer 1

To solve this problem, we can visualize a right triangle formed by the tree, its shadow, and the line connecting the top of the tree to the end of the shadow.

1. **Heights and Shadows**:
- The height of the tree (vertical leg of the triangle) is 24 feet.
- The length of the shadow (horizontal leg of the triangle) is 10 feet.

2. **Forming a Right Triangle**:
The right triangle has:
- One leg (tree height) = 24 feet
- Another leg (shadow length) = 10 feet

3. **Using the Pythagorean Theorem**:
According to the Pythagorean theorem, the relationship in a right triangle is given by:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the hypotenuse (the distance from the top of the tree to the end of the shadow), and \( a \) and \( b \) are the other two legs.

In this case:
- \( a = 24 \) feet (tree height)
- \( b = 10 \) feet (shadow length)

Plugging in the values:
\[
c^2 = 24^2 + 10^2
\]
\[
c^2 = 576 + 100
\]
\[
c^2 = 676
\]
Taking the square root to find \( c \):
\[
c = \sqrt{676} = 26
\]

4. **Final Result**:
The distance from the top of the tree to the top of its shadow is \( 26 \) feet.