Question

a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches. Find the angle between the diagonal of the box and the diagonal of its base. The angle should be measured in radiands

Answer 1

Answer:

0.7246 radians

Step-by-step explanation:

According to the Question,

Given that, a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches

• The length of the base diagonal (d) can be found using the Pythagorean theorem on length and width:

d = √{ (12)² +(15)² }  = √(144+225) = √369inches

• The tangent of the angle is the ratio of the height of the box to this length

 Tan∅ = 17/√369

Taking the $Tan^{-1}$ , we have

∅ = $Tan^{-1}$(17/√369) ≈ 0.7246 radians