To generate a new Pythagorean triple from an existing one, we can use the property of scaling by a factor. The given Pythagorean triple is \( (11, 60, 61) \).
To find a new Pythagorean triple that contains 183, we can determine the scaling factor \( k \) such that one of the elements in the triple (when scaled) equals 183.
Since 183 is the largest number (the hypotenuse) we're interested in, we can set \( 61k = 183 \):
\[ k = \frac{183}{61} = 3 \]
Now, we scale all elements of the original triple \( (11, 60, 61) \) by \( k = 3 \):
\[ (11 \cdot 3, 60 \cdot 3, 61 \cdot 3) = (33, 180, 183) \]
Therefore, the new Pythagorean triple that includes 183 is:
\[ (33, 180, 183) \]