Question

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

Answer 1

$d)\sin (C)=\frac{\sin (112)\cdot46}{47}$

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:

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

So let's cross multiply then:

$\begin{gathered} \frac{47}{\sin(112)}=\frac{46}{\sin(C)} \\ 47\cdot\sin (C)=46\cdot\sin (112) \\ \frac{47\cdot\sin (C)}{47}=\frac{46\cdot\sin (112)}{47} \\ \sin (C)=\frac{46\cdot\sin(112)}{47} \end{gathered}$

And that's the answer.