4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{23689deb-7eed-4022-848f-1278231a4056-10_547_1475_306_294}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of triangle \(A B D\) and triangle \(B C D\)
Given that
- \(A D C\) is a straight line
- \(B D = ( x + 3 ) \mathrm { cm }\)
- \(B C = x \mathrm {~cm}\)
- angle \(B D C = 30 ^ { \circ }\)
- angle \(B C D = 140 ^ { \circ }\)
- show that \(x = 10.5\) correct to 3 significant figures.
Given also that \(A D = ( x - 2 ) \mathrm { cm }\)
find the length of \(A B\), giving your answer to 3 significant figures.