3 The triangle \(A B C\), shown in the diagram, is such that \(A B = 5 \mathrm {~cm} , A C = 8 \mathrm {~cm}\), \(B C = 10 \mathrm {~cm}\) and angle \(B A C = \theta\).
- Show that \(\theta = 97.9 ^ { \circ }\), correct to the nearest \(0.1 ^ { \circ }\).
- Calculate the area of triangle \(A B C\), giving your answer, in \(\mathrm { cm } ^ { 2 }\), to three significant figures.
- The line through \(A\), perpendicular to \(B C\), meets \(B C\) at the point \(D\). Calculate the length of \(A D\), giving your answer, in cm , to three significant figures.