If $\sin A=\frac{1}{3}$ for an acute angle $A$, what is the value of $\cos A$?

If $\sin A=\frac{1}{3}$, take opposite side $=k$ and hypotenuse $=3k$. Then by Pythagoras theorem, adjacent side $=\sqrt{(3k)^2-k^2}=\sqrt{8k^2}=2\sqrt{2}k$. **Hence $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{2\sqrt{2}k}{3k}=\frac{2\sqrt{2}}{3}$.**