To determine the value of \( x \) in the Pythagorean triple \( (16, x, 34) \), we can use the Pythagorean theorem, which states that for a right triangle with sides \( a \), \( b \), and hypotenuse \( c \):
\[ a^2 + b^2 = c^2 \]
Here, let \( a = 16 \), \( b = x \), and \( c = 34 \). Thus, we can write the equation as:
\[ 16^2 + x^2 = 34^2 \]
Now, calculate \( 16^2 \) and \( 34^2 \):
\[ 16^2 = 256 \] \[ 34^2 = 1156 \]
Substituting these values into the equation gives:
\[ 256 + x^2 = 1156 \]
Next, isolate \( x^2 \) by subtracting \( 256 \) from both sides:
\[ x^2 = 1156 - 256 \] \[ x^2 = 900 \]
Taking the square root of both sides results in:
\[ x = \sqrt{900} = 30 \]
Since \( 16 < x < 34 \), we confirm \( x = 30 \) is within the specified range.
Therefore, the value of \( x \) is:
\[ \boxed{30} \]