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Radial SurveyRadial SurveyStage 6 - Year 12Stage 6 - Year 12

General Mathematic(HSC)

2

The Radial Survey (1/3)

A survey where angles and distances are measured from a point

030o

140o

245o

310o

N

45m

65m35m

50m

110o

105o65o

360o-310o+30o

80o

3

The Radial Survey – Perimeter (2/3)

030o

140o

245o

310o

45m

65m35m

50m

110o

105o65o

80o

d1

d2

d3

d4

d2 = a2 + b2 – 2ab Cos D

d12 = 502 + 452 – 2x50x45 Cos 80

d1 = 502 + 452 – 2x50x45 Cos 80

d1 ≈ 61.18482810

d1 ≈ 61 m

Repeat for dd22, dd33 and dd44.

dd22 ≈ 91 m dd33 ≈ 81 m

dd44 ≈ 47 m

Perimeter ≈ dd11++ dd2 2 ++ dd3 3 ++ dd44

≈ 61 + 91 +81 +47

≈ 280 m

4

The Radial Survey – Area (3/3)030o

140o

245o

310o

45m

65m35m

50m

110o

105o65o

80o

A1

A2

A3

A4

Area = ab x Sin C12

A1 = x 50 x 45 x Sin 8012

≈ 1107. 908722

≈ 1108

Repeat for AA22, AA33 and AA44.

AA22 ≈ 1374 m2 AA33 ≈ 1099 m2

AA44 ≈ 793 m2

Area ≈ AA11++ AA2 2 ++ AA3 3 ++ AA44

≈ 1108 + 1374 +1099 +793

≈ 4374 m2