The diagram shows a right triangle $\triangle DEF$, where $DE = 10$ ft and $AD = 6$ ft. $\overline{CD} = 3$ ft, and $\overline{CE} = 4$ ft. To solve for $\overline{EF}$, we can apply the Pythagorean theorem:

$DE^2 = AD^2 + EF^2$ Substitute the known values: $10^2 = 6^2 + EF^2$ $100 = 36 + EF^2$ $EF^2 = 100 - 36 = 64$ $EF = \sqrt{64} = 8 \text{ ft}$

The correct answer is $8$ ft, not 4 ft.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the Pythagorean theorem used for?
2. How would you solve a right triangle if only one side length and angles are given?
3. Can the Pythagorean theorem be used for non-right triangles?
4. What are real-life applications of the Pythagorean theorem?
5. How can you find the area of a right triangle?

Tip: The Pythagorean theorem only applies to right-angled triangles. Always ensure the angle is 90 degrees before using it!