# Angle and Survey Ft

Topics: Angle, Geometry, Normal distribution Pages: 16 (1264 words) Published: January 8, 2014
U N I T

2

BASIC SURVEY MATH
Edward Zimmerman, PLS
California Department of Transportation

Introduction
The purpose of this video unit is to present basic math concepts and principles useful to survey computations. It has been assumed that most viewers are already familiar with some or most of the topics presented in the beginning of the unit. It is important to have a developed understanding of the basic operations of arithmetic, algebra, geometry, and trigonometry. This unit is not designed as a complete math course, but rather as an overview and guide to computation processes unique to surveying and mapping. Surveyors who need to work on math operations and fundamental skills addressed in the video will find sources for further study in the reference section at the end of this unit.

Caltrans LS/LSIT Video Exam Preparation Course

Survey mathematics generally consists of applications of formulas and equations that have been adapted to work toward the specific needs of the surveyor such as:
• Units of measurement and conversions
• Check and adjustment of raw field data
• Closure and adjustment of survey figures
• Calculations for missing elements of a figure
• Working with coordinates (COGO)
• Intersections of straight lines and of circles
It is hoped this video unit will help viewers to recognize solution formats for problems and then make correct and effective use of appropriate methods to solve these particular survey problems.

Performance Expected on the Exams
Recognize solution formats, and make correct and effective use of appropriate mathematical solutions to particular survey applications.

Key Terms
Absolute value
Algebra

Arc

Arithmetic

Azimuth

Bearing

Central angle

Chord

Circular curve

Circumference

Complementary angle

Coordinate conversion

Cosecant

Cosine

Cotangent

Cubes

Decimal system

delta x, delta x

Departure

External distance

Geodetic north

2-2

Grid north

Basic Survey Math

Hexagon

Horizontal curve

Hypotenuse

Intersections

Intersection of straight line and arc

Intersections of straight lines

Inverse processes

Latitude

Law of cosines

Law of sines

Length of arc

Magnetic north

Meter

Mid-ordinate distance

Most probable value

Oblique triangle

Opposite side

Order of operations

Parabola

Parallelogram

Pentagon

Percent of slope

Percentage

pi

Plane geometry

Polar coordinates

Polygon

Pythagorean theorem

Random error

Rate of change

Rectangular coordinates

Residual

Rhomboid

Right triangle

Roots

Rounding off

Sag curve

Secant

Sector of a circle

Segment of a circle

Sexagesimal system

Signed numbers

Significant figures

Simultaneous equation

Sine

Square root

Squares

Standard error

Supplementary angles

US survey foot

Tangent

Trigonometry

2-3

Caltrans LS/LSIT Video Exam Preparation Course

Video Presentation Outline
Arithmetic
• Decimal system
• Rounding off and significant figures
• Percentage
• Squares, cubes and roots

Conversion of Units of Measure
• Converting lineal units
• Converting angular units
• Converting units of area

Random Error Analysis
• Error definitions
• Error residuals
• Statistical error matrix
• Propagation of error
• Error in summation
• Error in product
• Error in series

Algebra
• Signed numbers
• Equations
• Order of operations
• Parentheses
• Evaluating equations and combining terms
• Solving equations

2-4

Basic Survey Math

Plane Geometry
• Angles
• Geometrical theorems
• Geometrical figures
• Polygons
• Triangles

Trigonometry
• Right triangles
• Pythagorean theorem
• Trigonometric functions
• Oblique triangles
• Directions: bearings and...