Zadanie wykonam w załączniku
1 [latex]a)\ a=4\ sin alpha =0,8\ \ sin alpha alpha =frac{a}{c}\ 0,8=frac{4}{c}\ c=5\ \ b=sqrt{c^2-a^2}=sqrt{5^2-4^2}=sqrt{25-16}=sqrt{9}=3\ \ b)\ a=8\ tg alpha =1\ \ tg alpha =frac{a}{b}\ 1=frac{8}{b}\ b=8\ \ c=sqrt{a^2+b^2}=sqrt{8^2+8^2}=sqrt{128}=8sqrt{2}[/latex] 2 [latex]sin45^ocdot tg60^ocdot cos^230^o = frac{sqrt{2}}{2}cdot sqrt{3}cdot (frac{sqrt{3}}{2})^2=frac{sqrt{6}}{2}cdot frac{3}{4}=frac{3sqrt{6}}{8}[/latex] 3 [latex]a=4\ alpha = 30^o\ \ tg alpha =frac{b}{a}\ frac{sqrt{3}}{3}=frac{b}{4}\ b=frac{4sqrt{3}}{3}\ \ P=frac{1}{2}ab = frac{1}{2}cdot 4cdot frac{4sqrt{3}}{3}=frac{8sqrt{3}}{3} cm^2\ \ c=sqrt{a^2+b^2}=sqrt{4^2+(frac{4sqrt{3}}{3})^2}=sqrt{16+frac{48}{9}}=sqrt{frac{192}{9}}=frac{8sqrt{3}}{3}\ \ Ob=a+b+c = 4+frac{4sqrt{3}}{3}+frac{8sqrt{3}}{3}=4+frac{12sqrt{3}}{3}=4+4sqrt{3}}=\=4(1+sqrt{3}) cm[/latex] 4 [latex]sin30^o=frac{h}{a}\ frac{1}{2}=frac{h}{4}\ h=2\ \ P=ah=4cdot 2=8 [j^2]\ Ob=4a=4cdot 4=16 [j][/latex]
