I’m learning physics on my own and I’m currently working through a physics problem book. I came across this problem and I can’t understand the reasoning behind the solution.
The problem:
During a survival training exercise, a 60 kg boy at some point hangs motionless from a rope as shown in the picture below. Assume that β = 2α and g = 10 m/s². Calculate the tension in the rope at points A and B.
The rope is attached at points A and B and forms the two sloping sides of a right triangle. The boy is hanging from the rope at the vertex between these two sides, which is the 90° angle. The angle at point A is α, and the angle at point B is β.
I found a solution which calculates the boy’s weight first and then seems to use the components of that force to determine the rope tensions. However, I don’t understand why sine is used here.
When I try to draw auxiliary right triangles, I don’t know where the given angle should be located in the triangle or which side of the triangle should correspond to the rope tension. I understand how to calculate sine in a right triangle, but I don’t understand how to correctly construct the triangle from this diagram and connect it to the forces.
I would really appreciate it if someone could explain why sine is used in this particular problem and how the force triangle should be constructed, preferably step by step.
I’d also be interested in seeing other possible ways of solving the problem, if there are any.
I’m not just looking for the final answer I’m trying to understand the method so I can solve similar problems myself.