Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Radial Survey Stage 6 - Year 12 General Mathematic (HSC)

2 The Radial Survey (1/3) A survey where angles and distances are measured from a point 030 o 140 o 245 o 310 o N 45m 65m 35m 50m 110 o 105 o 65 o 360 o -310 o +30 o 80 o

3 The Radial Survey – Perimeter (2/3) 030 o 140 o 245 o 310 o 45m 65m 35m 50m 110 o 105 o 65 o 80 o d1d1 d2d2 d3d3 d4d4 d 2 = a 2 + b 2 – 2ab Cos D d 1 2 = – 2x50x45 Cos 80 d 1 = – 2x50x45 Cos 80 d 1 ≈ d 1 ≈ 61 m d 2 d 3 d 4 Repeat for d 2, d 3 and d 4. d 2 d 2 ≈ 91 m d 3 d 3 ≈ 81 m d 4 d 4 ≈ 47 m d 1 +d 2 + d 3 + d 4 Perimeter ≈ d 1 + d 2 + d 3 + d 4 ≈ ≈ 280 m

4 The Radial Survey – Area (3/3) 030 o 140 o 245 o 310 o 45m 65m 35m 50m 110 o 105 o 65 o 80 o A1A1 A2A2 A3A3 A4A4 Area = ab x Sin C 1212 A 1 = x 50 x 45 x Sin ≈ ≈ 1108 A 2 A 3 A 4 Repeat for A 2, A 3 and A 4. A 2 A 2 ≈ 1374 m 2 A 3 A 3 ≈ 1099 m 2 A 4 A 4 ≈ 793 m 2 A 1 +A 2 + A 3 + A 4 Area ≈ A 1 + A 2 + A 3 + A 4 ≈ ≈ 4374 m 2