In a right triangle on the unit circle, if \(\cos(\theta) = \frac{\sqrt{2}}{5}\), we can find \(\sin(\theta)\) using the Pythagorean identity:
\[ \sin^2(\theta) + \cos^2(\theta) = 1 \]
Substituting \(\cos(\theta)\):
\[ \sin^2(\theta) + \left(\frac{\sqrt{2}}{5}\right)^2 = 1 \]
Calculating \(\left(\frac{\sqrt{2}}{5}\right)^2\):
\[ \sin^2(\theta) + \frac{2}{25} = 1 \]
Now, isolate \(\sin^2(\theta)\):
\[ \sin^2(\theta) = 1 - \frac{2}{25} \]
Convert \(1\) to a fraction with a denominator of \(25\):
\[ \sin^2(\theta) = \frac{25}{25} - \frac{2}{25} = \frac{23}{25} \]
Now, take the square root to find \(\sin(\theta)\):
\[ \sin(\theta) = \sqrt{\frac{23}{25}} = \frac{\sqrt{23}}{5} \]
Now, we compare \(\sin(\theta) = \frac{\sqrt{23}}{5}\) with the given options (a. 1, b. 1/2, c. \sqrt{2}/2, d. \sqrt{3}/2). Since \(\frac{\sqrt{23}}{5}\) does not equal any of these options, it seems that none of the provided options reflect the correct value of the sine ratio.