Physics: force and motion

Resolve the string tensions vertically, we have, for situation of vertical equilibrium:
(T1).cos(45) + (T2).cos(60) = (500/1000)g ------------ (1)
where g is the acceleration due to gravity, taken to be 10 m/s^2

Resolve the tensions horizontally. For horizontal equilibrium, we have,
(T1).sin(45) = T2.(sin(60)
T2 = (T1).sin(45)/sin(60) ------------- (2)

Hence, equation (1) becomes,
(T1).cos(45) + (T1).sin(45).cos(60)/sin(60) = 0.5g
solve for T1 gives T1 = 4.48 N

From equation (2),
T2 = 4.48 x sin(45)/sin(60) N = 3.66 N

The answer is option D

Q: does Newton's first law states that an object at rest or constant velocity MUST have a zero net force??

A: This is Newton's Second Law, not First Law.