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Let T1 be the tension of the rope 30°; T2 be the tension of the rope 45°.
T1 and T2 are the magnitudes of the forces; their dimensions are newtons.
Force F1 has horizontal component T1*cos(30°) = .
Force F2 has horizontal component T2*cos(45°) = in opposite direction.
Equilibrium condition in horizontal direction gives you this equation
} = , or
= . (1)
Force F1 has vertical component T1*sin(30°) = .
Force F2 has vertical component T2*sin(45°) = .
Equilibrium condition in vertical direction gives you this equation
+ } = 20*g, or
+ = 40g. (2)
Thus you have a system of two equations (1) and (2), and now your task is to solve it.
For it, replace in equation (2) the term } by , based on equation (1).
You will get then
T1 + = 40g, or
= 40g,
T1 = .
From equation (1), you get then
T2 = = .
At this point, the problem is just solved.
If you want to get the numerical values for magnitudes / (tensions) T1 and T2, use your calculator.
Solved.