A75 lb weight hangs from a string as shown in the figure. find the tensions t1 and t2 in the string.

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Below is the solution:

T2cos(30) - T1cos(50) = 0
T1sin(50) + T2sin(30) - (75 lbs.)*(accel. grav.) = 0
T2cos(30) - T1cos(50) = 0 --> T1 = T2cos(30)/cos(50)

T1sin(50) + T2sin(30) - (75 lbs.)*(accel. grav.) = 0
(T2cos(30)/cos(50))sin(50) + T2sin(30) - (75 lbs.)*(accel. grav.) = 0 --> Solve for T2

T1 = -T1cos(50)i + T1sin(50)j
T2 = T2cos(30)i + T2sin(3)j

(T2cos(30)/cos(50))sin(50) + T2sin(30) - (75 lbs.)*(accel. grav.) = 0 --> T2[(cos(30)/cos(50))sin(50) + sin(30)] = 75*(grav) --> T2 = 75*grav/ [(cos(30)/cos(50))sin(50) + sin(30)]

T2 = 1566.49