The automatic flag$-$raising system on a horizontal flagpole attached to the vertical, outside wall of a tall building has become stuck. The management of the building wants to send a person crawling out along the flagpole to fix the problem. Because of your physics knowledge, you have been asked to consult with a group to decide whether or not this is possible.

You are all too aware that no one could survive the $80$m fall from the flagpole to the ground. The flagpole is a $60$ kg steel I$-$beam, which is very strong and rigid. One side of the flagpole is attached to the wall of the building by a hinge so that it can rotate vertically. The other end of the $3$ m long flagpole is attached to a strong, lightweight cable. The cable goes up from the flagpole at an angle of $30$ to the horizontal until it reaches the building where it is bolted to the wall. The mechanic who may be tasked with climbing out on the flagpole weighs $75$ kg including his equipment. From the specifications of the building construction, both the bolt attaching the cable to the building and the hinge have been tested to hold a vertical force of $1020$ N$.$

Your boss has decided that the worst case is when the mechanic is at the far end of the flagpole, three meters from the building, is this correct and is the mechanic safe?