I've been trying to solve the following statics problem dealing with suspension bridges:
Let d1=span length from tower to shore, let d2=mid-bridge span length (tower to tower). The main cable makes an angle of 24 degrees below horizontal to the top of the support tower on the d2 side and 30 degrees below horizontal to the top of the support tower on the d1 side. Ignore the mass of the cables and assume the bridge span is both uniform and perfectly horizontal. What must the ratio of d2 to d1 be so that the suspension cable exerts no net horizontal force on the towers?
I thought this was going to be a straight forward solution by calculating net forces on one tower for the horizontal axis but I end up with one equation two variables. Next, I tried algebraic methods using law of sines and assuming that the cable intersects the horizontal axis of the span at exactly mid-bridge so d2/2 is the value of one of the sides of the right triangle formed by the cable, the support tower and the half of the mid-span. This method resulted in an answer of 2.6. The correct answer is 3.8. I have no clue how to proceed next. Any help/hint would be appreciated.