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Find the angles that the diagonal of a rectangular parallelepiped 2 in. by 3 in. by 4 in. makes with the faces.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
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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| Photo by Math Principles in Everyday Life |
By using Pythagorean Theorem, the length of x is
By using Pythagorean Theorem, the length of d is
Therefore, the value of an angle is
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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| Photo by Math Principles in Everyday Life |
By using Pythagorean Theorem, the length of y is
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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| Photo by Math Principles in Everyday Life |
By using Pythagorean Theorem, the length of z is
Therefore, the value of an angle is
