To find the length of the third side in this right triangle, we can use the Pythagorean theorem:

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

where $a$ and $b$ are the lengths of the two legs, and $c$ is the length of the hypotenuse (the side opposite the right angle).

Given:

• One leg ($a$) = 3
• The hypotenuse ($c$) = 7

Substituting these values:

$3^2 + b^2 = 7^2$

$9 + b^2 = 49$

Now, isolate $b^2$:

$b^2 = 49 - 9$

$b^2 = 40$

Taking the square root of both sides:

$b = \sqrt{40} \approx 6.3$

So, the length of the third side is approximately 6.3 (rounded to the nearest tenth).

Would you like further details, or do you have any questions?

Here are five related questions to explore this concept further:

1. How would the solution change if the hypotenuse were 10 instead of 7?
2. What if both legs were given, but the hypotenuse was missing?
3. How can the Pythagorean theorem be used in three-dimensional space?
4. What are some real-life applications of the Pythagorean theorem?
5. How does trigonometry relate to the Pythagorean theorem?

Tip: In a right triangle, the hypotenuse is always the longest side, directly opposite the right angle.