need help with magnitude question

Question

A 700 pound object hangs from two cables with angles below the horizontal of $θ = 28$

Determine the magnitudes of the tension vectors, $| | {\vec{T}}_{1} | |$

John M. · Accepted Answer

Drawing T1 Tensor to the left at 28°, and T2 to the right at 47° and T3 hanging straight down with the 700 pound object.

The equations are:

Horizontal: T2Cos 47° - T1Cos 28° = 0

Vertical: T2Sin 47° + T1Sin48° = 700

Solving the 2 equations and 2 unknowns yields

T1 = 494.545 pounds

T2 = 640.300 pounds

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