The given image represents a right-angled triangle $\triangle KPN$, where:

• $\angle K = 90^\circ$
• $KN = 8$ (one leg)
• $PN = 10$ (hypotenuse)
• $KP = x$ (the other leg to be found)

To determine $x$, we can use the Pythagorean Theorem:

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

Substituting the given values:

$8^2 + x^2 = 10^2$

$64 + x^2 = 100$

$x^2 = 100 - 64$

$x^2 = 36$

$x = \sqrt{36} = 6$

Answer:

The missing side $KP = 6$.

Would you like a detailed explanation of the Pythagorean Theorem or any further clarifications?

Related Questions:

1. How can the Pythagorean Theorem be used in real-life applications?
2. What happens if the given triangle is not a right triangle?
3. How do you determine whether a triangle is a right triangle given its three sides?
4. What is the relationship between the Pythagorean Theorem and trigonometry?
5. How can you extend the Pythagorean Theorem to three dimensions?

Tip: The Pythagorean Theorem only applies to right triangles, so always check for a $90^\circ$ angle before using it!