To find the length of the third side in a right triangle, we can use the Pythagorean theorem. The formula is given by:

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

where $a$ and $b$ are the lengths of the legs of the triangle, and $c$ is the hypotenuse.

From the diagram:

• One leg is 2 units.
• The other leg is 3 units.

Since these two sides are the legs of the right triangle, we want to find the hypotenuse:

$2^2 + 3^2 = c^2$

Calculating:

$4 + 9 = c^2$ $13 = c^2$

Taking the square root of both sides:

$c = \sqrt{13}$

So, the length of the third side (the hypotenuse) in simplest radical form is:

$\sqrt{13}$

Would you like more details or have any questions?

Related Questions:

1. What is the Pythagorean theorem, and where does it apply?
2. How do you identify the hypotenuse in a right triangle?
3. Can the Pythagorean theorem be used in non-right triangles?
4. What are some examples of Pythagorean triples?
5. What is the distance formula in the coordinate plane?

Tip:

The Pythagorean theorem only works for right triangles—so always make sure the triangle has a right angle before applying it!