- Given that \(a\) and \(b\) are positive constants, solve the simultaneous equations
$$\begin{gathered}
a = 3 b ,
\log _ { 3 } a + \log _ { 3 } b = 2 .
\end{gathered}$$
Give your answers as exact numbers.
\section*{6.}
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{13c5a854-baea-4875-82bc-86a19c3be09c-08_687_454_294_703}
\end{figure}
Figure 1 shows 3 yachts \(A , B\) and \(C\) which are assumed to be in the same horizontal plane. Yacht \(B\) is 500 m due north of yacht \(A\) and yacht \(C\) is 700 m from \(A\). The bearing of \(C\) from \(A\) is \(015 ^ { \circ }\).
- Calculate the distance between yacht \(B\) and yacht \(C\), in metres to 3 significant figures.
The bearing of yacht \(C\) from yacht \(B\) is \(\theta ^ { \circ }\), as shown in Figure 1.
- Calculate the value of \(\theta\).