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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

Respuesta :

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 [tex]Tan^{-1}[/tex] , we have

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

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