Question

page 15 of 15 Solving Right Triangles Quick Check 3 of 53 of 5 Items 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) Responses 35 feet 35 feet 625 feet 625 feet 13.2 feet 13.2 feet 25 feet 25 feet Skip to navigation

Answer 1

To solve for the distance from the top of the flag pole to the tip of its shadow using the Pythagorean Theorem, we can represent the situation with a right triangle where:

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

Using the Pythagorean Theorem:

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

where:
- \( a \) is the height of the flag pole (20 feet),
- \( b \) is the length of the shadow (15 feet),
- \( c \) is the hypotenuse (the distance we want to find).

Substituting the values into the equation:

\[
20^2 + 15^2 = c^2
\]

Calculating the squares:

\[
400 + 225 = c^2
\]

\[
625 = c^2
\]

Taking the square root of both sides:

\[
c = \sqrt{625} = 25 \text{ feet}
\]

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

Therefore, the correct response is **25 feet**.