4 The diagram shows a triangle \(A B C\).
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The size of angle \(B A C\) is \(65 ^ { \circ }\), and the lengths of \(A B\) and \(A C\) are 7.6 m and 8.3 m respectively.
- Show that the length of \(B C\) is 8.56 m , correct to three significant figures.
- Calculate the area of triangle \(A B C\), giving your answer in \(\mathrm { m } ^ { 2 }\) to three significant figures.
- The perpendicular from \(A\) to \(B C\) meets \(B C\) at the point \(D\).
Calculate the length of \(A D\), giving your answer to the nearest 0.1 m .