Question

A 20-foot-tall flag pole casts a shadow that is 15 feet long. Which of the following correctly uses the Pythagorean Theorem to solve for the distance from the top of the flag pole to the tip of its shadow?(1 point)

Answer 1

To find the distance from the top of the flag pole to the tip of its shadow using the Pythagorean Theorem, you can visualize a right triangle where:

- The height of the flag pole (20 feet) represents one leg of the triangle.
- The length of the shadow (15 feet) represents the other leg of the triangle.
- The distance from the top of the flag pole to the tip of its shadow represents the hypotenuse of the triangle.

In this case, you can use the Pythagorean Theorem, which states that \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two sides.

Let:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
- \( c \) is the hypotenuse (the distance from the top of the flag pole to the tip of the shadow)

Thus, you have:
\[
20^2 + 15^2 = c^2
\]

Calculating that:
\[
400 + 225 = c^2
\]
\[
625 = c^2
\]

Now, taking the square root of both sides:
\[
c = \sqrt{625} = 25 \text{ feet}
\]

Therefore, the distance from the top of the flag pole to the tip of its shadow is 25 feet.