1 The triangle \(A B C\), shown in the diagram, is such that \(A B = 7 \mathrm {~cm} , A C = 5 \mathrm {~cm}\), \(B C = 8 \mathrm {~cm}\) and angle \(A B C = \theta\).
- Show that \(\theta = 38.2 ^ { \circ }\), 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.