Station $A$ is a control point with known coordinates $(E_A=1500\mathrm{.}000(m),N_A=600\mathrm{.}000(m))$ and

the line $AB$ has a known azimuth ${}_{AB}=45{00}^{\text{'}}{00}^{\text{'}\text{'}}.$

The following measurements are available:

$-,d_1=650\mathrm{.}000m,+-3cm$

$-,d_2=780\mathrm{.}000m+-4cm$

$-,{}_{BC}=60{00}^{\text{'}}{00}^{\text{'}\text{'}}+-{10}^{\text{'}\text{'}}$

Determine the best estimates of the

coordinates of stations $B(E_B,N_B)$

and $C(E_C,N_C)$ as well as the

corresponding correlation matrix.