The rectangular box shown in the figure has dimensions 9" * 5" * 3" (a = 9, b = 5, c = 3). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 5" * 3" side. (Round your answer to two decimal places.)

The simplest method to do this is with the vector dot product. Let the vector A = with magnitude √106 be the base diagonal, and B = be the diagonal vector on the side, with magnitude √34. Then cos θ = (A dot B) divided by the product of the magnitudes. A dot B = 30, so

cos θ = 30 / √ (34 x 106)

= 0.4997 = = >

θ = 49.19° is the answer