Physics question: a hammock is supported by two hooks at the same level...........?

Question

a hammock is supported by two hooks at the same level. a man is seated in this hammock. at what angle relative to the horizontal will the tension in each suspending rope ( hence the pull on each hook) be equal to the mans weight?

Answer 1

In a rope the force is acting in the direction of the rope.

For a given angle α to the horizontal you can separate the tension in an vertical and an horizontal part:
Fh = F·cos α
Fv = F·sin α

From a vertical force balance follows that the vertical part of the two suspending ropes must equal the weight of the man:
2 ·F·sin α = W

Moreover the magnitude of the tension in each rope should equal the weight of the man:
F = W

Hence:
2 ·W·sinα = W
<=>
sinα = 1/2
<=>
α = 30°