A uniform drawbridge must be held at a $34\mathrm{.}0$ angle above the horizontal to allow ships to pass underneath. The drawbridge weighs $45000$ NN$,$ is $14\mathrm{.}5$ mm long, and pivots about a hinge at its lower end. A cable is connected $3\mathrm{.}40$ mm from the hinge, as measured along the bridge, and pulls horizontally on the bridge to hold it in place.