How Do You Calculate Tension in Two Strings Holding a Mass?

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To calculate the tension in two strings holding a 100kg mass, one must consider the angles each string makes with the horizontal. The weight of the object is calculated using the equation w = m|g|. A free body diagram is recommended to visualize the forces acting on the mass, which include the tensions in both strings and the weight. By summing the forces in the x and y directions, two equations can be formed to solve for the tension in the first string (T1). Proper application of trigonometric functions for each tension will lead to the correct solution.
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Homework Statement


An object of mass 100kg is hanging from a ceiling by means of 2 strings. The 1st string (t1) makes an angle of 55 degree with the horizontal-right. The scond string 9T-2) makes an angle of 25 degree with horizontal left. Calculate tension in the first string (T1)


Homework Equations


w = m|g|

wx = w cos θw

wy = w sin θw =

T1x = T1 cos θT1 =

T1y = T1 sin θT1 =

T2x = T2 cos θT2 =

T2y = T2 sin θT2 =

T1x + T2x + wx =

T1 =

T1y + T2y + wy =


The Attempt at a Solution


I am stuck on this question. i have tried plugging in for the equations and none of the answers I have come up with are close to any of the choices. My professor is no help. Someone please explain this to me
 
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Try drawing a free body diagram of the forces acting on the block. Then, sum the forces in the x and y directions. You should have two expressions with which you can solve for T1.
 

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