Question

In a $\Delta ABC$, $a=2,b=3$ and $\sin A=\frac{2}{3}$. Then, $\cos C$ is equal to:

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{2}{\sqrt{3}}$
• D. $\frac{1}{\sqrt{13}}$

Answer 1

The correct option is B $\frac{2}{3}$

Using sine rule,

$\frac{a}{\sin A}=\frac{b}{\sin B}$

$\Rightarrow \frac{2}{2/3}=\frac{3}{\sin B}$

$\Rightarrow \sin B=1\Rightarrow B={90}^o$
So, $A+C={90}^0$

Hence $\cos C=\cos ({90}^o-A)=\sin A=\frac{2}{3}$