Question : If $\tan A=\frac{2}{3}$, then find $\sin A$.
Option 1: $\frac{1}{3}$
Option 2: $\frac{2}{\sqrt{13}}$
Option 3: $\frac{2}{3}$
Option 4: $\frac{3}{\sqrt{13}}$
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Correct Answer: $\frac{2}{\sqrt{13}}$
Solution :
Given, $\tan A=\frac{2}{3}$
Let perpendicular and base be 2 and 3 units.
Now, the hypotenuse $= \sqrt{2^2+3^2} = \sqrt{13}$ units
So, $\sin A = \frac{\text{perpendicular}}{\text{hypotenuse}}=\frac{2}{\sqrt{13}}$
Hence, the correct answer is $\frac{2}{\sqrt{13}}$.
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