Question1.

The Task

To calculate the length of the curved section in a road; AB in Fig 1. In Excel, create a reusable spreadsheet template to achieve this.

The Data

In Fig 1, AA’ and BB’ represent two straight tangential sections of a road linked by a smooth curve AB. Curve AB is represented by the arc of a circle centre O’: this is an offset-centred circle whose equation is given by x2 + y2 - 8x + 30y = 200.

The bearing of line BB’ is 79° 29'23'' and that of AA’ is 199° 45'16''.

Calculate the length of the arc AB, to a precision of 1mm.

Question 2.

The Task

To determine the coordinates of six points of a closed shape.

In Excel, create a reusable spreadsheet template to achieve this.

The Data

Angle and distance measurements have been made to six points (P, Q, A, R, S, T) from a point O. The angles are measured with respect to a reference point M, and are <MOP,<MOQ,<MOA,<MOR,<MOS,<MOT.

The distances are OP, OQ, OA, OR, OS, OT.