Question

Consider a triangle where A=80deg, a=2cm and b=4cm. How many possible triangles have the above properties? Write either 0, 1 or 2

Answer 1

I/m stuck on this problem. If i use a/sinA=b/sin ABC then 2/sin80=4/sinABC
what do i do next?

Answer 2

I guessed zero here as i came up with 1.96 for an answer but not sure how was suppose to come up with the zero.

Answer 3

\[\frac{2}{\sin(80)}=\frac{4}{\sin(ABC)}\]so:\[\sin(ABC)=2\sin(80)\approx1.96\]since values of the sine function must lie between -1 and 1, this implies there is no real solution to this. Therefore there are no possible triangles that can be created with these properties. Therefore, as you said, the answer is zero.