Răspuns:
[tex]\cos{MVP} = \frac{7}{9}[/tex]
Explicație pas cu pas:
In triunghiul isoscel VPM:
[tex]A = \frac{VO\times PM}{2} = \frac{VP\times VM \times \sin{MVP}}{2}\rightarrow\\\sin{MVP} = \frac{VO\times PM}{VP\times VM} = \frac{18\sqrt{2}\times 18}{27 \times 27} = \frac{2^2\times 3^4 \sqrt{2}}{3^6} = \frac{4\sqrt{2}}{9}[/tex]
[tex]\cos{MVP} = \sqrt{1 - sin^2(MVP)} = \sqrt{1 - \frac{32}{81}} = \sqrt{\frac{49}{81}}=\frac{\sqrt{49}}{\sqrt{81}} = \frac{7}{9}[/tex]
