The image you provided shows a right triangle with labeled sides. Here's what I see:

• The triangle has a right angle at vertex A.
• The length of one leg (adjacent to the right angle) is 12 units.
• The length of the hypotenuse is 20 units.
• The other leg, labeled as "X," is the side opposite to the right angle.

To solve for the length of the unknown leg (X), we can use the Pythagorean theorem, which states:

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

where:

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

Here, we have:

• $a = 12$
• $c = 20$
• We need to solve for $b = X$.

Substituting the known values into the Pythagorean theorem:

$12^2 + X^2 = 20^2$

$144 + X^2 = 400$

Now, subtract 144 from both sides:

$X^2 = 400 - 144 = 256$

Finally, take the square root of both sides:

$X = \sqrt{256} = 16$

So, the length of the missing leg is 16 units.

Would you like a more detailed explanation, or do you have other questions related to this problem? Here are some related questions:

1. How do we know when to use the Pythagorean theorem?
2. What if one of the sides had been negative? Could it still work in this context?
3. Can the Pythagorean theorem be applied to non-right triangles?
4. How do you calculate the perimeter of this triangle using the known sides?
5. What happens if the hypotenuse is shorter than one of the legs in a triangle?

Tip: The Pythagorean theorem is only applicable for right-angled triangles.