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15 September, 13:28

A rectangular box has length 9 inches, width 7 inches, and a height of 15 inches. find the angle between the diagonal of the box and the diagonal of its base. the angle should be measured in radians.

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  1. 15 September, 13:42
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    0.92085175 radians

    Let's first calculate the length of the diagonal of the base. Using the Pythagorean theorem:

    b = sqrt (9^2 + 7^2) = sqrt (81 + 49) = sqrt (130) = 11.40175425

    Now the length of the diagonal to the box. Once again, using the Pythagorean theorem:

    d = sqrt (15^2 + 11.40175425^2) = sqrt (225 + 130) = sqrt (335) = 18.84144368

    We now have a right triangle where we know the lengths of all three sides. The lengths are:

    a = 15

    b = sqrt (130) ≠11.40175425

    c = sqrt (335) ≠18.84144368

    we want the angle opposite to side a. So

    tan (A) = 15/11.40175425 = 1.315587029

    A = atan (1.315587029)

    A = 0.92085175 radians
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