[tex]\it cos C\ =\ cos30^o=\dfrac{\sqrt3}{2}\\ \\ \\ cosC=\dfrac{AC}{BC} \Rightarrow \dfrac{\sqrt3}{2}=\dfrac{12}{BC} \Rightarrow BC=\dfrac{2\cdot12}{\sqrt3}=\dfrac{^{\sqrt3)}4}{\ \ \sqrt3}=\dfrac{24\sqrt3}{3}=8\sqrt3\ cm[/tex]
Din teorema unghiului de 30°⇒ AB = BC/2 = 8√3/2 = 4√3 cm
AM este înălțime corespunzătoare ipotenuzei, dec:
[tex]\it AM=\dfrac{AB\cdot AC}{BC}=\dfrac{4\sqrt3\\\\cdot12}{8\sqrt3}=6\ cm[/tex]
[tex]\it\mathcal{P}_{ABC} =AB+BC+AC=4\sqrt3+8\sqrt3+12=12\sqrt3+12\ cm[/tex]
[tex]\it \mathcal{A}=\dfrac{c_1\cdot c_2}{2}=\dfrac{AB\cdot AC}{2}=\dfrac{4\sqrt3\cdot12}{2}=4\sqrt3\cdot6=24\sqrt3\ cm^2[/tex]
