__Category__: Solid Geometry"Published in Newark, California, USA"

Find the angles that the diagonal of a rectangular parallelepiped 1 in. by 3 in. by 5 in. make with the faces.

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

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Next, we need to draw a diagonal line at the top and bottom of the rectangular parallelepiped as well as its diagonal and angles as follows

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By using Pythagorean Theorem, the length of d is

Therefore, the value of an angle is

or

Next, we need to draw a diagonal line at the left and right of the rectangular parallelepiped as well as its diagonal and angles as follows

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Therefore, the value of an angle is

Next, we need to draw a diagonal line at the front and back of the rectangular parallelepiped as well as its diagonal and angles as follows

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Therefore, the value of an angle is

or