alleryIf $\sin A=\frac{1}{3}$ for an acute angle $A$, what is the value of $\cos A$?
A$\frac{2\sqrt{2}}{3}$
B$\frac{\sqrt{2}}{3}$
C$\frac{1}{\sqrt{3}}$
D$\frac{2}{3}$
Answer & Solution
Correct answer: A. $\frac{2\sqrt{2}}{3}$
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 $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{2\sqrt{2}k}{3k}=\frac{2\sqrt{2}}{3}$.**
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