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Someone with a mass of $60$ kg is sleeping in a hammock tied to a tree on each end with a rope. The two ropes form an angle of $45^\circ$ with the horizontal. How strong is the force through one of the ropes? If the angle was $30^\circ$, would the force be bigger?
We have
$\sin 45° = \cos 45° = \sqrt{2}/2$
We split our forces in horizontal and vertical components. The horizontal tensions must cancel each others, and the two vertical tensions must cancel the gravity force that pulls the person down.
$$T_1 \cos45° - T_2 \cos45° = 0$$ $$T_1 \sin45° + T_2 \sin45° = F_G = 60 \cdot 9.81$$
We get $T_1 = T_2 = F_G/(2 \cdot \sin45°)$
If we had an angle of $30^\circ$ we would have $\sin30^\circ < \sin45^\circ$ which implies $F_G/\sin30^\circ > F_G/\sin45^\circ$ so the tension through the rope would be bigger (and smaller for $60^\circ$)
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Thanks a lot for your help !