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 its shadow? apply a pythagorean triple to solve this problem

Answer 1

To find the distance from the top of the tree to the end of its shadow, we can use the Pythagorean theorem. In this case, we can treat the tree and its shadow as forming a right triangle where:

- The height of the tree (24 feet) is one leg of the triangle.
- The length of the shadow (10 feet) is the other leg of the triangle.
- The distance from the top of the tree to the tip of the shadow is the hypotenuse.

We can denote:
- \( a = 24 \) feet (height of the tree),
- \( b = 10 \) feet (length of the shadow),
- \( c \) (the distance from the top of the tree to the end of the shadow).

According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]

Substituting the known values:
\[
c^2 = 24^2 + 10^2
\]
\[
c^2 = 576 + 100
\]
\[
c^2 = 676
\]

Now, we take the square root of both sides to find \( c \):
\[
c = \sqrt{676}
\]
\[
c = 26
\]

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