Question

Help with question 13 ( the D just represents the word angle )

Answer 1

Using the law of sines, we would have that:

`(b)/(\sin B)=(c)/(\sin C)`

Solving for C,

`\begin{gathered} (b)/(\sin B)=(c)/(\sin C)\rightarrow(\sin C\cdot b)/(\sin B)=c\rightarrow\sin C\cdot b=c\cdot\sin B \\ \\ \rightarrow\sin C=(c\cdot\sin B)/(b)_{}\rightarrow C=\sin ^(-1)((c\cdot\sin B)/(b)_{}) \end{gathered}`

Plugging in the data given,

`\begin{gathered} C=\sin ^(-1)(((10.3)\cdot\sin (58.8))/((10.5))_{}) \\ \\ \Rightarrow C=57 \end{gathered}`

Therefore, we can conclude that: