[tex]a = \frac{ab \times ac \times \sin(a) }{2} \\ a = \frac{ab \times ac \times \sin(60) }{2} \\ a = \frac{7 \times 8 \times \frac{ \sqrt{3} }{2} }{2} \\ a = \frac{7 \times 4 \sqrt{3} }{2} = 14 \sqrt{3} {cm}^{2} \\ \\ a = \frac{ac \times bc \times \sin(c) }{2} \\ a = \frac{ac \times bc \times \sin(45) }{2} \\ a = \frac{12 \times 10 \times \frac{ \sqrt{2} }{2} }{2} \\ a = \frac{60 \sqrt{2} }{2} = 30 \sqrt{2} {dm}^{2} \\ \\ a = \frac{ab \times ac \times \sin(a) }{2} \\ a = \frac{ab \times ac \times \sin(30) }{2} \\ a = \frac{5 \times 8 \times \frac{1}{2} }{2} \\ a = \frac{20}{2} = 10 {m}^{2} [/tex]
