ENEV 281 – Chapter 3 - Surveying, Mapping, and Information Systems

This set covers basic mathematical concepts for surveying, including geometry, trigonometry, mensuration, and coordinate systems from Chapter 3.

Geometry

Derived from the phrase "earth measurement," this branch of mathematics is concerned with the properties of and relationships among lines, angles, surfaces, and solids.

Mensuration

The process of measuring and computing lengths or distances, surface areas, and volumes of solids.

Sum of Interior Angles Formula

$180^{\circ} \times (n - 2)$, where $n$ is the number of sides of a polygon.

Supplementary Angles

Two angles whose magnitudes add up to exactly $180^{\circ}$.

Perpendicular distance

The shortest distance from a point to a line, forming intersection angles of exactly $90^{\circ}$.

Perpendicular Bisector

A line that intersects another line at a right angle and divides it into two equal segments.

Alternate Interior Angles

Pairs of angles formed between parallel lines that are equal to one another.

Hypotenuse

Determined in a right triangle as the side opposite the right angle and is always the longest side.

Isosceles Triangle

A triangle where the altitude, or height, bisects both the vertex angle and the base.

Similar Triangles

Triangles in which corresponding angles are equal, such as triangle ABC and triangle DEF where angle $A =$ angle $D$ and angle $C =$ angle $F$.

Area of a Trapezoid

Calculated using the formula $\frac{a + b}{2} \times h$.

Trapezium

A quadrilateral in which no two sides are parallel.

Parallelogram

A four-sided polygon that can be oblique, rectangular, or square, with an area equal to $b \times h$.

Chord

Any straight line with both ends terminating on a circle.

Radius-Chord Property

A radius drawn perpendicular to a chord bisects both the chord and its intercepted arc.

Inscribed Angle

An angle whose size is equal to one-half the central angle subtended by the intercepted arc.

Tangent

A straight line that intersects a circle at exactly one point.

Segment of a Circle

An area equal to the area of the corresponding sector minus the area of the associated triangle.

Trigonometry

A field concerned with the relationships between the lengths of sides and the sizes of angles in a triangle.

Sine ($\sin A$)

The trigonometric ratio defined as $\frac{\text{side opposite } A}{\text{hypotenuse}}$.

Cosine ($\cos A$)

The trigonometric ratio defined as $\frac{\text{side adjacent } A}{\text{hypotenuse}}$.

Tangent ($\tan A$)

The trigonometric ratio defined as $\frac{\text{side opposite } A}{\text{side adjacent } A}$.

Versine ($\text{vers } A$)

A trigonometric function defined as $1 - \cos(A)$.

Exsecant ($\text{exsec } A$)

A trigonometric function defined as $\sec(A) - 1$.

Obtuse Angle

An angle that exceeds a measurement of $90^{\circ}$.

Law of Sines

The mathematical relationship expressed as $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

Law of Cosines

The mathematical relationship expressed as $a^2 = b^2 + c^2 - 2bc \cos(A)$ (or its equivalents for sides $b$ and $c$).

Polar Coordinates

A system where the location of a point is expressed by a distance ($r$) and an angle ($A$).

Parallels of Latitude

Lines that run in an east-west direction, are parallel to one another, and measure distance north or south from the Equator.

Meridians of Longitude

Lines that run in a north-south direction, are farthest apart at the Equator, meet at the poles, and measure distance east or west of the prime meridian.