Twierdzenie pitagorasa mowi, ze suma kwadratow przyprostokatych trojkata prostokatnego jest rowna kwadratowi przeciwprostokatnej.
[tex]a^2+b^2=c^2\\\\a) \\a = 11\\b = 10\\c = x\\11^2+10^2=x^2\\121+100=x^2\\221=x^2\\x=\sqrt{221}[/tex]
[tex]b) \\a = 2\sqrt3\\b = 4\\c = y\\(2\sqrt3)^2+4^2=y^2\\4*3+16=y^2\\12+16=y^2\\28=y^2\\y=\sqrt{28} = \sqrt{2*2*7}=4\sqrt{7}[/tex]
[tex]c)\\a = 3\sqrt6\\b = x\\c = 12\\(3\sqrt6)^2+x^2=12^2\\9*6+x^2=144\\54+x^2=144 /-54\\x^2=90\\x=\sqrt{90} = \sqrt{9*10}=3\sqrt{10}[/tex]
Zad. 1
[tex]1l = 1dm^3\\\\1dm = 10cm\\1m = 10dm\\\\V = Pp * H\\Pp = ab\\\\a = 15dm\\b = 0,8m = 8dm\\H = 100cm = 10dm\\Pp = 15dm*0.8dm=12dm^2\\V = 12dm^2*10dm=120dm^3\\\\H_2 = \frac45*10dm=8dm\\\\V_2=12dm^2*8dm=96dm^3\\\\96dm^3=96l[/tex]
Odp. Nalezy wlac 96l wody.
