Hello, classicstrings!
The diagram is quite impossible . . . They lied to us! Code:
C
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b=4 * * a
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* 60° *
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A c=6 B
Law of Cosines: .$\displaystyle a^2\:=\:b^2 + c^2 - 2bc\cos A$
We have: .$\displaystyle a^2\:=\:4^2 + 6^2 - 2\cdot4\cdot6\cos60^o\:=$ $\displaystyle \:28\quad\Rightarrow\quad a \,= \,\sqrt{28} \,= \,2\sqrt{7}$
Law of Sines: .$\displaystyle \frac{\sin B}{b}\,=\,\frac{\sin A}{a}$
We have: .$\displaystyle \frac{\sin B}{4}\,=\,\frac{\sin60^o}{2\sqrt{7}}\quad \Rightarrow\quad \sin B \:=\:\frac{4\sin60^o}{2\sqrt{7}}\:=\:0.654653671$
Therefore: .$\displaystyle B\;=\;\sin^{-1}(0.654653671)\:=\:$ $\displaystyle 40.839339654 \quad\Rightarrow\quad B \:\approx \:41^o$
See? . . . and they told us that $\displaystyle B\,=\,50^o$