Question

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

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

Answer 1

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

Using sine rule:
$\frac{a}{\sin A}=\frac{b}{\sin B}$
$\Rightarrow \frac{2}{2/3}=\frac{3}{\sin B}$
$\Rightarrow \sin B=1\Rightarrow B={90}^{\circ }$
So, $A+C={90}^{\circ }$
$\Rightarrow \cos C=\cos (90-A)=\sin A=\frac{2}{3}$