Rysunek pomocniczy w zalaczniku.
a)
[tex]D = 10\\cos\alpha = \frac25\\\frac{a}D = cos\alpha\\\frac{a}D=\frac25\\\frac{a}{10}=\frac25\\a=\frac{10*2}5=2*2=4[/tex]
[tex]d = a\sqrt2\\d^2+H^2=D^2\\(a\sqrt2)^2+H^2=D^2\\2a^2+H^2=D^2\\H^2=D^2-2a^2\\H=\sqrt{D^2-2a^2}\\H=\sqrt{10^2-2*4^2}\\H=\sqrt{100-2*16}\\H=\sqrt{100-32}\\H=\sqrt{64}=8[/tex]
[tex]V=Pp*H\\Pp = a^2\\V=a^2*H\\V=4^2*8\\V=16*8=128j^3[/tex]
b)
[tex]cos\beta = \frac{d}{D'}\\a^2+H^2=D'^2\\4^2+8^2=D'^2\\16+64=D'^2\\D'^2=\sqrt{80}=\sqrt{16*5}=4\sqrt5\\d=a\sqrt2=4\sqrt2\\cos\beta=\frac{4\sqrt2}{4\sqrt5}=\frac{4\sqrt2*\sqrt5}{4*5}=\frac{\sqrt2*\sqrt5}{5}=\frac{\sqrt{10}}5[/tex]
