1. A triangle $A B C$ is given with sides $A B = a$ and $B C = \sqrt { 3 } a$. Which of the following statements is correct?\\
– If $A \hat { C } B = \frac { \pi } { 6 }$, then the triangle is right-angled;\\
– If the triangle is right-angled, then $A \hat { C } B = \frac { \pi } { 6 }$.\\
Justify your answers.\\