Question

A 30 foot tall tree casts a shadow that is 16 feet long. What is the distance from the top of the tree to the top of it's shadow?



Apply a A 30 foot tall tree casts a shadow that is 16 feet long. What is the distance from the top of the tree to the top of it's shadow?

Apply a Pythagorean triple to solve this problem.

Answer 1

To find the distance from the top of the tree to the top of its shadow, we can treat this situation as a right triangle.

1. **Identify the triangle**:
- The height of the tree forms one leg of the triangle, which is 30 feet.
- The length of the shadow forms the other leg, which is 16 feet.
- The distance we are trying to find is the hypotenuse (\(d\)).

2. **Pythagorean theorem**:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this can be stated as:
\[
a^2 + b^2 = c^2
\]
where:
- \(a = 30\) feet (height of the tree)
- \(b = 16\) feet (length of the shadow)
- \(c = d\) (distance from the top of the tree to the top of the shadow)

3. **Plug in the values**:
\[
30^2 + 16^2 = d^2
\]

4. **Calculate the squares**:
\[
900 + 256 = d^2
\]
\[
1156 = d^2
\]

5. **Take the square root to find d**:
\[
d = \sqrt{1156}
\]
\[
d = 34
\]

Therefore, the distance from the top of the tree to the top of its shadow is **34 feet**.