I've been given the following question:
The answer book states that the area of $\triangle ABC$ is $19.4cm^2$ and $\angle BDA$ is $52.16 ^ \circ$:
My understanding is that the $\sin$ law, when used to find angles, can provide 2 solutions. I found $\angle BDA$ to be $127.8 ^ \circ$ and the area of $\triangle ABC$ to be $13.47cm^2$. In the diagram the angle $\angle BDA$ is clearly obtuse, so I don't understand why I'm wrong.
Am I missing something or is there an error in the answer booklet?