| r29 vs r32 | ||
|---|---|---|
| ... | ... | |
| 55 | 55 | [math(\displaystyle \begin{aligned} \cos{B}=\frac{a^2+c^2-b^{2}}{2ac} \end{aligned} )] 로 하고, |
| 56 | 56 | |
| 57 | 57 | 이때, [math(\sin^{2}{B}+\cos^{2}{B}=1)]이니 [math(\sin {B}= 1- \cos {B})] 를 얻어서 다음을 만든다. |
| 58 | ||
| 59 | [math(\displaystyle \begin{aligned} \triangle {\rm ABC}&=\dfrac{1}{2}ac\sin{B} =\dfrac{1}{2}ac \sqrt{1-\left(\frac{a^2+c^2-b^{2}}{2ac} \right)^{2}} \end{aligned} )] | |
| 60 | ||
| 61 | [math(\displaystyle \begin{aligned} \triangle {\rm ABC}&= \dfrac{1}{4}\sqrt{4a^{2}c^{2}-(a^2+c^2-b^{2})^{2}} \end{aligned} )] | |
| 62 | ||
| 63 | [math(\displaystyle \begin{aligned} \triangle {\rm ABC}& = \dfrac{1}{4}\sqrt{[ (a+c)^{2}-b^{2} ] [ b^{2}-(a-c)^{2} ]} \\&= \dfrac{1}{4}\sqrt{ (a+b+c)(a+c-b) (a+b-c)(b+c-a) } \end{aligned} )] |