clear
clc

L1 = 0.3;
L2 = 0.3;
L3 = 0.3;

D1 = 0.2;
D2 = 0.2;
D3 = 0.3;

Theta1 = 30;
Theta2 = 30;
Theta3 = 30;

Rb = 0.4;
Re = 0.2;

syms Ex Ey Ez

eqn1 = L1^2 == (cosd(Theta1)*Rb + D1 - Ex - Re)^2 + (-Ey)^2 + (-sind(Theta1)*Rb - Ez)^2;
eqn2 = L2^2 == (cosd(Theta2)*(-Rb/2) + D2 - Ex - Re)^2 + ((3^(1/2)*Rb)/2 - Ey)^2 + (-sind(Theta2)*(-Rb)/2 - Ez)^2;
eqn3 = L3^2 == (cosd(Theta3)*(-Rb/2) + D3 - Ex - Re)^2 + (-(3^(1/2))*Rb/2 - Ey)^2 + (-sind(Theta3)*(-Rb)/2 - Ez)^2;

eqns = [eqn1 eqn2 eqn3];

soln = solve(eqns,[Ex Ey Ez],'ReturnConditions',true);

E_abs = [abs(soln.Ex); abs(soln.Ey); abs(soln.Ez)];
E = [vpa(E_abs(1)); vpa(E_abs(3)); vpa(E_abs(5))]