Find smallest angle θ for rope not to break with archaeologist at midpoint

[Payne0511]

Homework Statement

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope . The rope will break if the tension in it exceeds 2.80×10^4 N, and our hero's mass is 91.0 kg.

What is the smallest value the angle \theta can have if the rope is not to break?

Homework Equations

Tension=(M*g)/cos(theta)

The Attempt at a Solution

I was able to find the tension on the rope to be 2260 N. from there I thought I could set the above equation >= to the maximum tension of the rope 28000 N and solve for theta, which gave me 1.54, but that was clearly wrong. Not too sure what else to try here..

thanks

 

[kuruman]

How is theta defined, with respect to the vertical or horizontal? However it is defined, draw a free body diagram. There are three forces acting on the mass, the weight and two pieces of the rope. Your expression does not have a factor of 2 in it.