Question

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.)

Answer 1

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to
`0.6155` radian

Explanation:

Please see the attached image for better understanding

Length of OB is equal to

`√(19^2 + 19^2 )`

`19√(2)`

Now the length of OE is equal to

`√(19^2 + 19^2 + 19^2 ) = 19 √(3)`

Now Angle BOE is equal to

`cos^(-1) ((722)/(19√(2)* 19√(3) )) = 0.6155` radians

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to
`0.6155` radian