To determine the value of \( x \) in the Pythagorean triple \( (20, x, 29) \), we use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse. In this case, \( c = 29 \), \( a = 20 \), and \( b = x \), so we can write the equation as:
\[ 20^2 + x^2 = 29^2 \]
Calculating \( 20^2 \) and \( 29^2 \):
\[ 20^2 = 400 \] \[ 29^2 = 841 \]
Now substituting these values into the equation:
\[ 400 + x^2 = 841 \]
Subtracting 400 from both sides gives:
\[ x^2 = 841 - 400 \] \[ x^2 = 441 \]
Now take the square root of both sides:
\[ x = \sqrt{441} \] \[ x = 21 \]
Since \( x < 29 \), the value of \( x \) is \( 21 \).
Thus, the value of \( x \) is \(\boxed{21}\).