A $$10.0-kg$$ monkey climbs a uniform ladder with weight $$1.20\times 10^2\ N$$ and length $$L=3.00\ m$$ as shown in figure $$P12.24$$. The ladder rests against the wall and makes an angle of $$\theta =60.0^o$$ with the ground. The upper and lower ends of the ladder rest on frictionless surface. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only $$80.0\ N$$.
Find the tension in the rope when the monkey is two-thirds of the way up the ladder.