To find the missing side \( A \) of the right triangle, we can use the Pythagorean theorem, which states:
\[ A^2 + B^2 = C^2 \]
Here, we have:
- \( B = 6 \)
- \( C = 34 \)
Plugging in these values into the equation gives:
\[ A^2 + 6^2 = 34^2 \]
Calculating \( 6^2 \) and \( 34^2 \):
\[ 6^2 = 36 \] \[ 34^2 = 1156 \]
Now substitute these values into the equation:
\[ A^2 + 36 = 1156 \]
To find \( A^2 \), subtract 36 from both sides:
\[ A^2 = 1156 - 36 \] \[ A^2 = 1120 \]
Now take the square root of both sides to find \( A \):
\[ A = \sqrt{1120} \]
Calculating \( \sqrt{1120} \):
\[ A \approx 33.5 \]
Rounding to the nearest tenth, the length of side \( A \) is:
\[ \boxed{33.5} \]