第14章 14.3

(1)

$C = 180 - 39 - 64 = 77°$

$a = b\frac{\sin A}{\sin B} = 32\frac{\sin 39°}{\sin 64°} = 22$

$c = b\frac{\sin C}{\sin B} = 32\frac{\sin 77°}{\sin 64°} = 35$

(2)

$a^2 = b^2 + c^2 - 2bc\cos A = 47^2 + 52^2 - 2 \cdot 47 \cdot 52 \cdot \cos 69° = 3161 \qquad a = 56$

$\sin B = \frac{b}{a}\sin A = \frac{47}{56}\sin 69° = 0.78 \qquad B = 51°$

$C = 180 - 69 - 51 = 60°$

(3)

$\cos A = \frac{-a^2 + b^2 + c^2}{2bc} = \frac{-34^2 + 89^2 + 118^2}{2 \cdot 89 \cdot 118} = 0.985 \qquad A = 10°$

$\cos B = \frac{a^2 - b^2 + c^2}{2ac} = \frac{34^2 - 89^2 + 118^2}{2 \cdot 34 \cdot 118} = 0.892 \qquad B = 27°$

$C = 180 - 10 - 27 = 143°$