三角比の総復習③（面積・正弦定理・余弦定理）

$$S=\frac{1}{2}bc\sin A$$

$$S=\frac{1}{2}bc\sin B$$

$$S=\frac{1}{2}bc\sin C$$

$$\frac{15}{2}$$

$$\frac{5}{2}$$

$$30$$

$$27\sqrt{3}$$

$$21\sqrt{3}$$

$$\frac{a}{\sin A}=\frac{b}{\sin B}$$

$$\frac{b}{\sin B}=\frac{c}{\sin C}$$

$$\frac{a}{\sin A}=\frac{c}{\sin C}$$

$$\frac{b}{\sin C}=\frac{c}{\sin B}$$

$$b\sin B=c\sin C$$

$$b\sin C=c\sin B$$

$$b\sin30\degree\ =8\sin135\degree\$$

$$b\sin135\degree\ =8\sin30\degree\$$

$$b\times\ \frac{1}{\sqrt{2}}=8\times\ \frac{\sqrt{3}}{2}\$$

$$b\times\ \frac{1}{\sqrt{2}}=8\times\ \frac{1}{2}\$$

$$b=8$$

$$b=4\sqrt{2}$$

$$a^2=b^2+c^2-2bc\cos A$$

$$b^2=c^2+a^2-2ca\cos B$$

$$c^2=a^2+b^2-2ab\cos C$$

$$c^2=3+5-2\times3\times5\cos120\degree\$$

$$c^2=3^2+5^2-2\times3\times5\cos120\degree\$$