Hi alexandertg6! Welcome to PF!
Quote by alexandertg6
a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle θ = 70° with the vertical. The tension in the cable is 500 N. Find the gravitational force on the beam in unit vector notation and the force on the beam from the hinge in unit vector notation.
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T = .5(horizontal distance) ( gravity) (mass)/ vertical distance
500 = (.5(9.8)(12sin70)m)/(12cos70)

hmm … you've taken moments about the hinge
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but what's 12sin70º ?