This problem shows a right triangle, and we need to find the length of the third side, which is the hypotenuse. The given sides are 7 and 8, which are the legs of the right triangle.

We can apply the Pythagorean theorem, which states:

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

Where:

• $a = 7$ (one leg),
• $b = 8$ (the other leg),
• $c$ is the hypotenuse (the third side we are solving for).

Let's calculate:

$c^2 = 7^2 + 8^2$

$c^2 = 49 + 64$

$c^2 = 113$

Now, solve for $c$:

$c = \sqrt{113} \approx 10.630$

Rounding to the nearest tenth:

$c \approx 10.6$

So, the length of the third side is approximately 10.6.

Would you like more details on the steps? Feel free to ask! Here are some related questions:

1. How does the Pythagorean theorem apply to other triangle types?
2. What if one side is unknown and it's not a right triangle—what would you do?
3. Can the Pythagorean theorem be applied in 3D shapes like pyramids?
4. How is the Pythagorean theorem related to trigonometric functions?
5. What are other ways to calculate the sides of a triangle?

Tip: Always double-check the rounding instructions to ensure you're rounding to the correct decimal place.