A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{2}{\sqrt{13}}\]
D) \[\frac{1}{\sqrt{13}}\]
E) \[\frac{2}{3}\]
Correct Answer: E
Solution :
\[a=2,b=3,\sin A=\frac{2}{3}\Rightarrow {{\sin }^{2}}A=\frac{4}{9}\] \[\therefore \] \[{{\cos }^{2}}A=1-{{\sin }^{2}}A=\frac{5}{9}\] \[\Rightarrow \] \[\cos A=\frac{\sqrt{5}}{3}\] By sine rule \[\frac{\sin A}{a}=\frac{\sin B}{b}\] \[\Rightarrow \] \[\frac{2}{3}\times \frac{1}{2}=\frac{\sin B}{3}\] \[\Rightarrow \] \[\sin B=1\]\[\Rightarrow \]\[B=90{}^\circ \] In\[\Delta ABC,\] \[\cos C=\frac{a}{b}=\frac{2}{3}\]You need to login to perform this action.
You will be redirected in
3 sec