Solving Tension Problem: 45° & 75° Angles, 55N Weight

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To solve the tension problem involving a 55N weight suspended by two ropes at 45° and 75° angles, start by resolving the tension forces into their vertical and horizontal components. Apply the equilibrium condition, where the sum of vertical forces must equal zero, leading to the equation T1*sin(45°) + T2*sin(75°) = 55N. For horizontal forces, set T1*cos(45°) equal to T2*cos(75°) to establish a second equation. Solve this system of equations step by step to find the tensions in both ropes. Understanding vector resolution and equilibrium principles is crucial for tackling similar physics problems effectively.
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How would you solve a problem as follows:

There is a 55N weight suspended by two ropes. The ropes make angles of 45 and 75 degrees with the ceiling. Determine the tension in the two ropes.


I've tried a few things but none have worked. Vectors test tomorrow and these type of questions kill me. Any help is most appreciated! Preferably step by step :)
 
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1. A vector, here the tension, can be resolved into 2 component vectors that makes your calculation easier.
2. For vector of same or opposite direction, simple arithmetics can be applied.
3. For a body in equilibrium, the net forces in any direction equal to zero.

From above you can deduce equations with given data.
 
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