Radial Survey Maths PDF

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Summary

Progress on raduis of maths in the university feild...

Description

Radial Survey - (Plane Table Radial Survey) A Radial survey is used to create a diagram to represent a piece of land, where we take measurements; both distance and angle size (usually using bearings) form a central point. In a plane table survey, the angles drawn are always accurate but the distances are not drawn to scale.

Paddock

Table Paper

Conducting a Radial Survey 1. A table is placed in a field with a large sheet of paper. 2. A point is marked in the centre of the sheet of paper and labelled O 3. A line is drawn from the centre, O, along the line of sight to each corner of the field or paddock. This may be known as the radial line. 4. The distance from O on the paper to the corner of the field is measured and recorded along the line on the sheet of paper. (This may be drawn to scale on the diagram but is not essential. 5. Step 4 is repeated for each corner of the area being surveyed. 6. Boundary lines are drawn to replicate the shape of the field. 7. Angles marked at the centre of the page are measured and recorded using a compass. These angles may be marked at the centre or as bearings at each corner.

93° 60°

90° 117°

Bearings at the end of the lines

Angles marked at the centre

Example A radial survey of a section of land is shown below:

a)

Find the size of ∠𝑃𝑂𝐿. ∠𝑃𝑂𝐿 = (360 − 327) + 41 = 33 + 41 = 74

b)

Find the area of triangle POL to the nearest square metre 1

Use formula 𝐴 = 2 𝑎𝑏 sin 𝐶 1

𝐴 = 2 × 30 × 24 sin 74° 𝐴 = 346 𝑚2 c)

Find the length of the boundary PN Use formula 𝑐 2 = 𝑎2 + 𝑏 2 − 2𝑎𝑏 cos 𝐶 𝑐 2 = 302 + 262 − 2 × 30 × 26 cos 89°...