(a) Cosine rule: \(AC=\sqrt{8.7^2+11.4^2-2(8.7)(11.4)\cos119^\circ}=17.37287\ldots\text{ cm}\), rounding to 17.37. (b) Sine rule in ACE: \(\sin AEC=AC\sin20^\circ/10.9\). The diagram requires the obtuse angle, so \(AEC=180^\circ-\sin^{-1}(AC\sin20^\circ/10.9)\). Then \(ACE=180^\circ-20^\circ-AEC=\boxed{13.0^\circ}\). (c) In right triangleADC, \(AD=AC\sin ACE\), \(CD=AC\cos ACE\). Thus perimeter=\(8.7+11.4+AD+CD=\boxed{40.9\text{ cm}}\), using unrounded AC and ACE.