6 The diagram shows a triangle \(A B C\).
The lengths of \(A B , B C\) and \(A C\) are \(8 \mathrm {~cm} , 5 \mathrm {~cm}\) and 9 cm respectively.
Angle \(B A C\) is \(\theta\) radians.
- Show that \(\theta = 0.586\), correct to three significant figures.
- Find the area of triangle \(A B C\), giving your answer, in \(\mathrm { cm } ^ { 2 }\), to three significant figures.
- A circular sector, centre \(A\) and radius \(r \mathrm {~cm}\), is removed from triangle \(A B C\). The remaining shape is shown shaded in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{e183578a-29a8-4112-b941-06c8894ed078-14_467_677_1462_685}
Given that the area of the sector removed is equal to the area of the shaded shape, find the perimeter of the shaded shape. Give your answer in cm to three significant figures.
[0pt]
[6 marks]