3 zadania do rozwiazania. Zadania w zaloczniku: zad 6,7,9. Prosze o rozwiazanie

6. [latex]tgalpha=frac{2sqrt3}{3}[/latex] [latex]frac{sinalpha}{cosalpha}=frac{2sqrt3}{3}[/latex] [latex]sinalpha= frac{2sqrt3}{3} cosalpha[/latex] [latex]frac{3sinalpha+sqrt3cosalpha}{2sinalpha-2cosalpha}=[/latex] [latex]frac{3 cdot frac{2sqrt3}{3} cosalpha+sqrt3cosalpha}{2 cdot frac{2sqrt3}{3} cosalpha-2cosalpha}=frac{2sqrt3cosalpha+sqrt3cosalpha}{frac{4sqrt3}{3} cosalpha-2cosalpha}=[/latex] [latex]frac{cosalphaleft(2sqrt3+sqrt3 ight) }{cosalphaleft(frac{4sqrt3}{3}-2 ight) }=frac{3 sqrt{3} cosalpha}{frac{4sqrt3-6}{3}cosalpha}=[/latex] [latex]frac{3 sqrt{3}}{frac{4sqrt3-6}{3}}=frac{9sqrt{3}}{4sqrt3-6}=frac{9sqrt{3}}{2(2sqrt3-3)}=[/latex] [latex]frac{9sqrt{3}(2sqrt3+3)}{2(2sqrt3-3)(2sqrt3+3)}=frac{54+27 sqrt{3} }{2 cdot (12-9)}=[/latex] [latex]frac{27(2+sqrt{3})}{2 cdot 3}=frac{9(2+sqrt{3})}{2}[/latex] ============================== 7. [latex]P=2sqrt3[/latex] [latex]b=2sqrt2[/latex] [latex]P=frac{b^2sinalpha}{2}[/latex] [latex]frac{(2sqrt2)^2sinalpha}{2}=2sqrt3 / cdot 2[/latex] [latex]8sinalpha=4sqrt3 /:8[/latex] [latex]sinalpha= frac{ sqrt{3} }{2}[/latex] [latex]180^o-alpha=60^o[/latex] [latex]alpha=180^o-60^o[/latex] [latex]alpha=120^o[/latex] ============================== 9. a=3 b=6 c=7 Obliczam połowę obwodu [latex]p= frac{a+b+c}{2}[/latex] [latex]p= frac{3+6+7}{2}[/latex] [latex]p= frac{16}{2}[/latex] [latex]p=8[/latex] Obliczam pole [latex]P=sqrt{p(p-a)(p-b)(p-c)}[/latex] [latex]P=sqrt{8 cdot (8-3) cdot (8-6) cdot (8-7)}[/latex] [latex]P=sqrt{8 cdot 5 cdot 2 cdot 1}[/latex] [latex]P=sqrt{80}[/latex] [latex]P=4sqrt{5}[/latex]