Physics Problem?

Question

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 2.10×10^4 N , and our hero's mass is 91.1 Kg.
1) If the angle between the rope and the horizontal is 10.6, find the tension in the rope.
Take the free fall acceleration to be = 9.80 m/ s^2
2430 N Correct
2) What is the smallest value the angle can have if the rope is not to break?

I found the answer to the first question, but for osme reason i can not get the answer tothe second one. I did some calculation and got it to be 4.8 but it says that is not the correct answer.

Any help will be appreciated

thanks

answer was 1.22 degree

Answer 1

Sum of vert =0= -W+2T sin(10.6)
T=W/(2 sin(10.6))
T=mg/(2 sin(10.6)=
T=2426.7N

Working the problem in reverse

Angle = arcSin(mg/2T)=
Angle= arcSin(91.1 x 9.8/(2 x 2.1 e 4))=
Angle =0.62 degrees (if my computations are correct)