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## Sagot :

[tex]\[ \sin^2 (\theta) + \cos^2 (\theta) = 1 \][/tex]

Given:

[tex]\[ \cos (\theta) = \frac{3}{10} \][/tex]

First, we square the cosine value:

[tex]\[ \cos^2 (\theta) = \left(\frac{3}{10}\right)^2 = \frac{9}{100} \][/tex]

Next, we use the Pythagorean identity to find [tex]\(\sin^2 (\theta)\)[/tex]:

[tex]\[ \sin^2 (\theta) = 1 - \cos^2 (\theta) \][/tex]

[tex]\[ \sin^2 (\theta) = 1 - \frac{9}{100} = \frac{100}{100} - \frac{9}{100} = \frac{91}{100} \][/tex]

Now, to find [tex]\(\sin (\theta)\)[/tex], we take the square root of both sides:

[tex]\[ \sin (\theta) = \sqrt{\sin^2 (\theta)} \][/tex]

[tex]\[ \sin (\theta) = \sqrt{\frac{91}{100}} = \frac{\sqrt{91}}{10} \][/tex]

Thus, the correct answer is:

[tex]\[ \boxed{\frac{\sqrt{91}}{10}} \][/tex]

So, the correct answer is option D:

D. [tex]\(\frac{\sqrt{91}}{10}\)[/tex]