To find the missing leg of a right triangle when you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.
In your case:
- \(c = 20, \text{cm}\) (hypotenuse)
- \(a = 12, \text{cm}\) (one leg)
- \(b\) is the missing leg.
Plugging in the values, we get:
\[ 12^2 + b^2 = 20^2 \]
Calculating the squares:
\[ 144 + b^2 = 400 \]
Now, subtract 144 from both sides:
\[ b^2 = 400 - 144 \] \[ b^2 = 256 \]
Now, take the square root of both sides to find \(b\):
\[ b = \sqrt{256} \] \[ b = 16, \text{cm} \]
So, the missing leg is 16 cm.