Question

If the measure of angle B = 35

degrees, a = 43, and c = 19, then
find the measure of angle C.

Answer 1

Using the Law of Cosihes,

`b^2 = a^2 +c^2 -2ac \cos B \\ \\ b^2 = 43^2 + 19^2 - 2(43)(19)(\cos 35^(\circ)) \\ \\ b=\sqrt{43^2 + 19^2 - 2(43)(19)(\cos 35^(\circ)} \\ \\ b=\sqrt{2210-1634 \cos 35^(\circ)}</p><p>`

Using the Law of Sines,

`(\sin A)/(a)=(\sin B)/(b) \\ \\ \sin A=(a \sin B)/(b) \\ \\ \sin A=\frac{43 \sin 35^(\circ)}{\sqrt{2210-1634 \cos 35^(\circ)}} \\ \\ A=\sin^(-1)\left(\frac{43 \sin 35^(\circ)}{\sqrt{2210-1634 \cos 35^(\circ)}} \right), 180^(\circ)- \sin^(-1)\left(\frac{43 \sin 35^(\circ)}{\sqrt{2210-1634 \cos 35^(\circ)}} \right) \\ \\ \\ \implies \angle C=145-\sin^(-1)\left(\frac{43 \sin 35^(\circ)}{\sqrt{2210-1634 \cos 35^(\circ)}} \right), \sin^(-1)\left(\frac{43 \sin 35^(\circ)}{\sqrt{2210-1634 \cos 35^(\circ)}} \right)-35^(\circ)`