Question

Two observation posts A and B are 12 km apart. A third observation post C is located 15 km from A such that CBA is 67º. Find the measure of CÂB

Answer 1

Using the law of sines:

`\begin{gathered} (AB)/(\sin(C))=(AC)/(\sin (B)) \\ so\colon \\ \sin (C)=(AB\cdot\sin (B))/(AC) \\ \sin (C)=(12\cdot\sin (67))/(15) \\ C=\sin ^(-1)((12\cdot\sin(67))/(15)) \\ C\approx47.43^(\circ) \end{gathered}`

Using the triangle sum theorem:

`\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ so\colon \\ x+47.43+67=180 \\ x=180-67-47.43 \\ x=m\angle C=m\angle CAB=65.57^(\circ) \end{gathered}`