(1 point) a rectangular box has length 3 inches, width 13 inches, and a height of 4 inches. find the angle between the diagonal
of the box and the diagonal of its base. the angle should be measured in radians.
1 answer:
The length of the base diagonal (d) can be found using the Pythagorean theorem on length and width:
... d = √((3 in)² +(13 in)²) = √(9+169) in = √178 in
The tangent of the angle you want to find is the ratio of the height of the box to this length:
... tan(α) = 4/√178
Taking the arctangent, we have
... α = arctan(4/√178) ≈ 0.291285 radians
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Step-by-step explanation:
the proof is given above
