Rog-sadee

Rog-sadee jechuun danaa ji’oomeetirii sarara qajeelaa sadii fi guttiyyoo(vertex) sadii irraa hojjetame dha.

Shallaggii naannoo roga sadii

Dheerinni cinaachaa roga sadii a, b fi c yoo ta’u kofoon α, β fi γ dha.	: 1.1. $s=a+b+c$ ${\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}.$ $c^{2}\ =a^{2}+b^{2}-2ab\cos(\gamma )$ $b^{2}\ =a^{2}+c^{2}-2ac\cos(\beta )$ $a^{2}\ =b^{2}+c^{2}-2bc\cos(\alpha )$ $\alpha =\arccos \left({\frac {b^{2}+c^{2}-a^{2}}{2bc}}\right)$ $\beta =\arccos \left({\frac {a^{2}+c^{2}-b^{2}}{2ac}}\right)$ $\gamma =\arccos \left({\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right)$

$\mathrm {Area} ={\frac {1}{2}}bh$	: 1.1. $\mathrm {Area} ={\frac {1}{2}}bh$ Bal’inni bal’ina, b cinaacha kamiyyuu roga saddeetii agarsiisa, h immoo olka’iinsa cinaacha kana irraa gara golee faallaatti perpendikulaariin kaafame agarsiisa. $Area={\frac {1}{2}}ab\sin \gamma ={\frac {1}{2}}bc\sin \alpha ={\frac {1}{2}}ca\sin \beta$ $Area={\frac {1}{2}}ab\sin(\alpha +\beta )={\frac {1}{2}}bc\sin(\beta +\gamma )={\frac {1}{2}}ca\sin(\gamma +\alpha ).$ $Area={\frac {b^{2}(sin\alpha )(sin(\alpha +\beta ))}{2sin\beta }}$ $Area={\frac {a^{2}}{2(cot\beta +\cot \gamma )}}={\frac {a^{2}(sin\beta )(sin\gamma )}{2sin(\beta +\gamma )}}$ $Area={\sqrt {s(s-a)(s-b)(s-c)}}$ As $s={\frac {a+b+c}{2}}$ Mee guddinni kofa 3 walakkaa naannoo ta’uu isaa haa hubannu $Area={\frac {1}{4}}{\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}$ $Area={\frac {1}{4}}{\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}$ $Area={\frac {1}{4}}{\sqrt {(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}}.$

Rogsadeen kofa sirri kan ballinni kofa saa 90 madaalkofa(digrii)

Rogsadeen kofqoree kan ballinni kofa isaa >90 madaalkofa(digrii)

Rogsadeen kofa jufunfula kan ballinni kofa saa <90 madaalkofa(digrii)


Rogsadee kofasirri	Rogsadee jufunfula (Obtuse)	Rogsadee kofqoree(acute)
	$\quad \underbrace {\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad } _{}$
	Habalakaa (Obliikii)