To find the length of the third side of this right triangle, we can apply the Pythagorean theorem, which states:

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

where:

• $a$ and $b$ are the legs of the right triangle, and
• $c$ is the hypotenuse (the longest side).

From the diagram:

• One leg $a = 16$,
• The hypotenuse $c = 20$.

We need to find the missing leg $b$. Plugging the values into the Pythagorean theorem:

$16^2 + b^2 = 20^2$

This simplifies to:

$256 + b^2 = 400$

Now subtract 256 from both sides:

$b^2 = 400 - 256 = 144$

Taking the square root of both sides:

$b = \sqrt{144} = 12$

So, the length of the third side is 12.

Would you like more details or have any questions? Here are some related questions you could explore:

1. How would you apply the Pythagorean theorem if both legs were unknown, but the hypotenuse was known?
2. What if the triangle had sides 16 and 12, how would you find the hypotenuse?
3. How would the Pythagorean theorem change if the triangle was not a right triangle?
4. Could you use trigonometry (like sine or cosine) to find the missing side in a right triangle?
5. What are some real-world applications of the Pythagorean theorem?

Tip: Always double-check if the triangle is a right triangle before using the Pythagorean theorem.