[tex]a^{2} =b^{2} +c^{2} -2bc*cos\alpha[/tex]
[tex]25=36+49-2*42*cos\alpha[/tex]
[tex]30=42cos\alpha[/tex]
[tex]cos\alpha =\frac{30}{42}[/tex]
[tex]sin^{2}\alpha =1-cos^{2} \alpha[/tex]
[tex]sin^{2} \alpha = \frac{1764}{1764} - \frac{900}{1764}[/tex]
[tex]sin^{2} \alpha = \frac{864}{1764}[/tex]
[tex]sin\alpha =\frac{12\sqrt{6} }{42} =\frac{2\sqrt{6} }{7}[/tex]
[tex]P=\frac{1}{2}*6*7*\frac{2\sqrt{6} }{7} =6\sqrt{6}[/tex]
[tex]P=\frac{abc}{4R}[/tex]
[tex]R=\frac{abc}{4P} =\frac{210}{24\sqrt{6} } =\frac{35}{4\sqrt{6} }=\frac{35\sqrt{6} }{24}[/tex]
[tex]p=\frac{a+b+c}{2}=9[/tex]
[tex]P=rp=9r[/tex]
[tex]r=\frac{P}{9} =\frac{6\sqrt{6} }{9} =\frac{2\sqrt{6} }{3}[/tex]
