### Problem (3)

Given the horizontal network below:

The initial coordinates of point W are estimated.

Create the **[C]** and **[K]** matrices.

#### Solution

The coordinates are large and manipulating them could lead to potential rounding errors. To simplify computations a bit, the coordinates can be reduced to a local origin. This is done by subtracting one constant from the E coordinates and another from the N. In this case, subtract 42,600 m from E coordinates and 115,000 m from N:

Point | E | N |

A | 67.034 | 835.802 |

B | 70.147 | 1161.493 |

C | 313.231 | 1062.610 |

W | 200 | 1000 |

**Matrices structures**

**Distances and angles from initial approximations**

**[K] matrix elements**

**Compute [C] matrix elements**

*Distance WA*

*Distance WC*

*Angle AWB*

*Angle BWC*

*Assemble [C] and [K] matrices.*

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