Question

(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.

Answer 1

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