g (1 point) Find the angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians. (Hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

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podgorica podgorica · Answer 1 · 2021-02-13T13:35:11+01:00

Answer:

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to [tex]0.6155[/tex] radian

Step-by-step explanation:

Please see the attached image for better understanding

Length of OB is equal to

[tex]\sqrt{19^2 + 19^2 }[/tex]

[tex]19\sqrt{2}[/tex]

Now the length of OE is equal to

[tex]\sqrt{19^2 + 19^2 + 19^2 } = 19 \sqrt{3}[/tex]

Now Angle BOE is equal to

[tex]cos^{-1} (\frac{722}{19\sqrt{2}* 19\sqrt{3} }) = 0.6155[/tex] radians

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to [tex]0.6155[/tex] radian