Let's consider a problem involving a right triangle and the Pythagorean theorem:

Problem:

You have a right triangle with one leg of length 6 units and another leg of length 8 units. Find the length of the hypotenuse.

Solution:

In a right triangle, the relationship between the legs and the hypotenuse is given by the Pythagorean theorem:

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

Where:

• $a$ and $b$ are the lengths of the legs,
• $c$ is the length of the hypotenuse.

In this case, $a = 6$ and $b = 8$. Substituting these values into the equation:

$6^2 + 8^2 = c^2$ $36 + 64 = c^2$ $100 = c^2$ $c = \sqrt{100}$ $c = 10$

So, the length of the hypotenuse is 10 units.

---

Do you want more details or have any questions?

Here are 5 related problems for further practice: 1