Question

Cosinus de unghiul format de planele vad si vbc.
ab=18
vo=18√2
vm=vp= apotema piramidei= 27​

Answer 1

Răspuns:

$\cos{MVP} = \frac{7}{9}$

Explicație pas cu pas:

In triunghiul isoscel VPM:

$A = \frac{VO\times PM}{2} = \frac{VP\times VM \times \sin{MVP}}{2}\rightarrow\\\sin{MVP} = \frac{VO\times PM}{VP\times VM} = \frac{18\sqrt{2}\times 18}{27 \times 27} = \frac{2^2\times 3^4 \sqrt{2}}{3^6} = \frac{4\sqrt{2}}{9}$

$\cos{MVP} = \sqrt{1 - sin^2(MVP)} = \sqrt{1 - \frac{32}{81}} = \sqrt{\frac{49}{81}}=\frac{\sqrt{49}}{\sqrt{81}} = \frac{7}{9}$