giscourses.cfans.umn.educogo coordinate geometry cogo involves directly entering the …direct data...

Direct Data Entry

•COGO – Coordinate geometry

•COGO involves directly entering the

coordinates measured in the field,

•Coordinates may be tagged with attribute data

in the field, e.g. well depth or pressure, when

their locations are measured

Survey instrument for collection of

coordinate geometry data

Theodolite or Transit –

measurement of horizontal and

vertical angles

Level – measurement of vertical

angles

Electronic Distance Meter -

measurement of distance

Total Station – measurement of

angles and distances

azimuth distance X Y

p0 10128.3 6096.4

p1 32.4 122

p2 91.7 207

P3 123.3 305

P4 212.5 193

P5 273.9 206

P6 355.5 145

Given a Table of Azimuths and Distances, What are the Coordinates?

P0

P1 P2

P3

P4

P5

P6

sine (a) = A/Hcosine (a) B/Htangent (a) A/B

op

po

site

sid

e

adjacent side

Direct Data Entry

•Data then down-loaded to computer, ingested

by the GIS software, and processed to form a

spatial data layer.

•To date, surveying-based COGO has proven

too expensive for most natural resource

applications

•GPS (discussed later) increasingly common

for COGO

_____ Direction ?

_____

Degrees ?

Azimuth Angle_____

Degrees ?

_____

Degrees ?

Label direction and 0, 90, 180 and 270 Degrees

Draw a 42 degree azimuth; Draw a 256 degree azimuth

NORTH

90°

Azimuth Angle180°

270°

Label direction and 0, 90, 180 and 270 Degrees

Draw a 42 degree azimuth; Draw a 256 degree azimuth

~42°

~256°

0°

SOH - CAH - TOAIt is pronounced "so - ka - toe - ah".

SOH - CAH - TOAIt is pronounced "so - ka - toe - ah".

The SOH stands for "Sine of an angle is Opposite over Hypotenuse."The CAH stands for "Cosine of an angle is Adjacent over Hypotenuse."The TOA stands for "Tangent of an angle is Opposite over Adjacent."

http://wright.nasa.gov/airplane/trig.html

Adjacent

Op

po

site

Sine(a) = A/H

Solve for A Sine(a) x H = A

Cosine(a) = B/H

Solve for B Cosine(a) x H = B

Since you knowH (the hypotenuse or distance)And the angle “a” then

Using COGO; if given an angle and distance from a point, “PO” then calculate the coordinates of “P1”

Calculate the x, y of “P1”

Sine(a) = A/H

Solve for A Sine(a) x H = A

Cosine(a) = B/H

Solve for B Cosine(a) x H = B

Since you knowH (the hypotenuse or distance)And the angle “a” then

Use Table or Calculator

Lookup value for angle

57.6°

33.3°

Given10,128.3 = x6,096.4 = y

WORKSHEET

Lecture Question? What are the coordinates of xn, yn?

Name_____________

Background Concepts

122

65.4

103.0

65.4

103.0

57.6°

33.3°

Given xn = 10,400.6 and yn = 6,193.3, azimuth of 123.3° and distance of 305What is (xr,yr)?

305

123.3°

NEW QUESTION

-167.5

254.9

(10,655.5, 6,025.8)

57.6°

33.3°

10,334.9 6,021.6