Let's solve the problem:

The diagram shows a right triangle, with the hypotenuse being 26 ft, the base being 10 ft, and the height (the flagpole) as the unknown.

Using the Pythagorean Theorem:

$a^2 + b^2 = c^2$

Where:

• $a$ is the height (the flagpole, unknown),
• $b$ is the base ($10$ ft),
• $c$ is the hypotenuse ($26$ ft).

Step 1: Substitute known values

$a^2 + 10^2 = 26^2$

$a^2 + 100 = 676$

Step 2: Solve for $a^2$

$a^2 = 676 - 100$ $a^2 = 576$

Step 3: Find $a$ by taking the square root

$a = \sqrt{576} = 24$

Final Answer:

The height of the flagpole is 24 ft.

Let me know if you'd like further clarification!

Related Questions:

1. How is the Pythagorean Theorem applied in real-world scenarios?
2. What are other ways to verify triangle dimensions if the Pythagorean Theorem doesn’t apply?
3. What is the geometric significance of the hypotenuse in a right triangle?
4. Can the flagpole's height be measured directly without calculations in this problem?
5. Why is it important to check the units when solving problems like this?

Tip:

Always confirm whether the triangle in question is a right triangle before applying the Pythagorean Theorem.