A cable rigging must be run from the ground through the top of a guidepost 8 feet high, and continue in a straight line to the face of a building that stands 16 feet from the post along the ground.
If the length of the cable is to be minimized, what angle θ should it make with the face of the building?

Question

anonymous · Answer

I got theta=arctan( (16/18)^(1/3))
but apparently that's wrong

anonymous · Answer

|dw:1351963816768:dw|

phi · Answer

|dw:1351975590297:dw|
used pythagoras, replaced x and y with functions of tan theta
took the derivative with respect to theta, and set to zero
I got an ugly 4th degree.  with x= tan theta
x^4 + 2x^3 -2x -4=0
one real, positive root is x= $\sqrt[3]{2}$
this give theta about 51.561 degrees