Question

A 29 ft long rope is tied to the top of a flag pole. The rope is staked to the ground 21 ft away from the base of the pole. How tall is the flag pole?
Responses

A 20 ft20 ft

B 28 ft28 ft

C 32 ft32 ft

D 36 ft36 ft

E 50 ft

Answer 1

To find the height of the flag pole, we can use the Pythagorean theorem. The scenario describes a right triangle where:

- The length of the rope (hypotenuse) is 29 ft.
- The distance from the base of the pole to the stake (one side of the triangle) is 21 ft.
- The height of the pole (the other side of the triangle) is what we are trying to find.

According to the Pythagorean theorem:

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

Where:
- \(c\) is the hypotenuse (29 ft),
- \(a\) is one of the legs (21 ft), and
- \(b\) is the other leg (the height of the flag pole, which we will denote as \(h\)).

Plugging in the known values:

\[
21^2 + h^2 = 29^2
\]

Calculating \(21^2\) and \(29^2\):

\[
441 + h^2 = 841
\]

Now, subtract 441 from both sides to isolate \(h^2\):

\[
h^2 = 841 - 441
\]
\[
h^2 = 400
\]

Taking the square root of both sides to solve for \(h\):

\[
h = \sqrt{400}
\]
\[
h = 20
\]

Therefore, the height of the flag pole is **20 ft**.

The correct answer is:

**A 20 ft**.