Question

In any triangle ABC, if c=30°,b= 4, a=2 find A and B.​

Answer 1

Using the Law of Cosines,

`c^(2)=2^(2)+4^(2)-2(2)(4)(\sin 30^(\circ))\\\\c^(2)=12\\\\c=2√(3)`

Using the Law of Sines,

`(\sin A)/(a)=(\sin C)/(c)\\\\(\sin A)/(2)=(\sin 30^(\circ))/(2√(3))\\\\(\sin A)/(2)=(1)/(4√(3))\\\\\sin A=(1)/(2√(3))\\\\A=\boxed{\sin^(-1) \left((1)/(2√(3)) \right)}`

So, as angles in a triangle add to 180 degrees,

`B=180^(\circ)-30^(\circ)-\sin^(-1) \left((1)/(2√(3)) \right)\\\\B=\boxed{150^(\circ)-\sin^(-1) \left((1)/(2√(3)) \right)}`