The rectangular box shown in the figure has dimensions 10" × 7" × 3" (a = 10, b = 7, c = 3). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 7" × 3" side. (Round your answer to two decimal places.)

Answer 1

That is the angle between the vectors (7,10,0) and (7,0,3)
So since

(7,10,0)•(7,0,3) = √149√58 cosθ,
cosθ = 49/√8642 = 0.527