Mathematics for GIS Professionals
|Angles are used in daily life. Engineers and architects use angles for designs, roads, buildings and sporting facilities. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas. Artists use their knowledge of angles to sketch portraits and paintings.
An angle is shown below.
Lines AB and AC meet at the point A to form an angle. The point A is the vertex of the angle, and the lines that meet to make the angle are called the arms of the angle.
The amount of turn from one arm of the angle to the other is said to be the size of an angle.
A degree is defined such that the angle of one full turn (or circle) is 360 degrees.
A protractor is used to measure angles. In this section, we will consider the use of a protractor that has the shape of a semi-circle and two scales marked from 0º to 180º.
We use the inner scale to measure the angle ABC, as the arm AB passes through the zero of the inner scale. Following the inner scale around the protractor, we find that the other arm, BC, passes through the inner scale at 60º. So, the size of angleABC is 60 degrees. We write this as follows:
We use the outer scale to measure the angle PQR, as the arm PQ passes through the zero of the outer scale. Following the outer scale around the protractor, we find that the other arm, QR, passes through the outer scale at 120º. So, the size of angle PQR is 120 degrees. We write this as follows:
Angles are classified according to their size.
Note that a right angle is marked on the diagram as a small square.
A protractor can be used to measure the size of an acute angle (between 0º and 90º) and an obtuse angle (between 90º and 180º).
To measure the reflex angle PQR, extend the arm PQ to A to form angle PQA which is a straight angle. Then measure the size of the angle AQR and add 180º.