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30 March, 07:22

Find the angle between a diagonal of a cube and a diagonal of one of its faces.

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  1. 30 March, 07:36
    0
    35.26°

    Step-by-step explanation:

    If a cube has side length x

    diagonal of the face = x*√2

    The diagonal of the cube = x * √3

    the angle between them is an acute angle in a right triangle,

    opposite = x, adjacent = x*√2, hyp. = x*√3

    sin (angle) = x / (x*√3)

    angle = sin^ (-1) (1/√3) = 35.26
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