Question

In triangle ABC, if c = 46, b = 47....

Answer 1

`d)\sin (C)=(\sin (112)\cdot46)/(47)`

1) In this question, the best way to tackle it is to sketch out that triangle:

2) Let's use The Law of Sines and then perform some algebraic manipulation:

`\begin{gathered} (b)/(\sin(B))=(c)/(\sin(C)) \\ (47)/(\sin(112))=(46)/(\sin (C)) \end{gathered}`

So let's cross multiply then:

`\begin{gathered} (47)/(\sin(112))=(46)/(\sin(C)) \\ 47\cdot\sin (C)=46\cdot\sin (112) \\ (47\cdot\sin (C))/(47)=(46\cdot\sin (112))/(47) \\ \sin (C)=(46\cdot\sin(112))/(47) \end{gathered}`

And that's the answer.