Question

A rectangular box has length 9 inches, width 7 inches, and a height of 15 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

0.92085175 radians  
Let's first calculate the length of the diagonal of the base. Using the Pythagorean theorem:
 b = sqrt(9^2 + 7^2) = sqrt(81 + 49) = sqrt(130) = 11.40175425 
 Now the length of the diagonal to the box. Once again, using the Pythagorean theorem:
 d = sqrt(15^2 + 11.40175425^2) = sqrt(225 + 130) = sqrt(335) = 18.84144368 
 We now have a right triangle where we know the lengths of all three sides. The lengths are:
 a = 15
 b = sqrt(130) ≠11.40175425
 c = sqrt(335) ≠18.84144368
 
 we want the angle opposite to side a. So
 tan(A) = 15/11.40175425 = 1.315587029
 A = atan(1.315587029)
 A = 0.92085175 radians