第14章 14.5

(1)

cosA=a2+b2+c22bc=4+9+1624=2124=78\cos A = \frac{-a^2+b^2+c^2}{2bc} = \frac{-4+9+16}{24} = \frac{21}{24} = \frac{7}{8}

cosB=a2b2+c22ac=49+1616=1116\cos B = \frac{a^2-b^2+c^2}{2ac} = \frac{4-9+16}{16} = \frac{11}{16}

cosC=a2+b2c22ab=4+91612=312=14\cos C = \frac{a^2+b^2-c^2}{2ab} = \frac{4+9-16}{12} = -\frac{3}{12} = -\frac{1}{4}

cosA:cosB:cosC=78:1116:14=14:11:4\cos A : \cos B : \cos C = \frac{7}{8} : \frac{11}{16} : -\frac{1}{4} = 14 : 11 : -4

解説: r31bn1z