Question

In order to unload clay easily, the body of a dump truck must be elevated to at least 45°. The body of a dump truck that is 12 feet long has been raised to 8 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer

Answer 1

Assume that the angle is at the rear of the truck bed, and that the length of the truck bed is 12'.  Then:
          
                    opp side
tan theta = --------------
                    adj side

becomes:
                        8 ft
tan theta    = ---------    = 2/3 = approx.  0.667   
                       12 ft

Then tan theta = 2/3, and arctan (2/3) = 0.589 radian, or 33.7 degrees.

This is less than 45 deg, so the answer is NO, the clay will not pour out easily.