This document provides an overview of the history and applications of units of angles. It defines what an angle is and discusses positive and negative angles. It describes the degree and radian units of measuring angles and provides examples of different types of angles classified by degree measure such as acute, right, obtuse, and straight angles. It explains how radians are defined in relation to circles. Finally, it lists several applications of angle measurement in fields like athletics, construction, engineering, and astronomy and provides specific examples of how angles are used in activities like football, basketball, architecture, and fitting furniture.

1. History &
Applications of
Units of Angles
PRESENTED BY:
UMAR FAROOQ
DEPARTMENT OF POL. SCI.
& IR
UNIVERSITY OF GUJRAT

2. Overview
• Angle
• Positive and Negative Angle
• Units of Angles
• Degree
• Types of Angles
• Radians
• Applications of Units of Angles
• References

3. • If I draw a line starts from a point and goes indefinitely in one direction, it is
called a ray.
• Some commonly used terms in angles are:
• Initial side: the original ray
• Terminal side: the final position of the ray after rotation
• Vertex: The point where the two rays intersect
• Angle can be define as some measures between two rays.
• Two rays meet at one point to form an angle.
Angle

4. • An angle is said to be a positive angle if the direction of rotation is anticlockwise.
• The angles which are measured clockwise from the base are called negative angles.
Positive and Negative Angle

5. There are several units for measuring angles. Here we look at;
1. Degree
2. Radian
Units of Angles

6. • Degrees are a unit of angle measure. A full circle is divided into 360 degrees, then the angle is
made by each part is 1°. For example, a right angle is 90 degrees. Or
• A degree is a measurement of plane angle, representing 1⁄360 of a full rotation, so one full circle is
360°; one degree is equivalent to π/180 radians.
• A degree usually denoted by °.
• Degrees may be further divided into minutes and seconds.
Degree

7. Based on the degree of measurement, the angles are classified as:
 Zero Angle: An angle whose measure is 0°
 Acute Angle: An angle which is greater than 0° and less than 90°
 Right Angle: Any angle which is equal to 90°
Types of Angles

8.  Straight Angle: An angle which is equal to 180°.
 Obtuse Angle: An angle which is greater than 90° but less than 120°.
 Complete Angle: An angle whose measure is 360 °.
Types of Angles

9. • A radian is the measure of central angle that subtends an arc of length ‘s’ equal to the radius ‘r’ of
the circle.
• This ratio will give you the radian measure of the angle.
• The circumference of the entire circle is 2π, so it follows that 360° equals 2π radians. Hence,
1° equals π/180 radians
And
1 radian equals 180/π degrees
Radians

10. Angles are used in daily life. Following are some applications of units of angles
 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.
 Construction, architecture, sports, engineering, art, dance etc. make use of the concept of angles.
 Scientists and astronomers depend on the angles that celestial bodies make to study their movement
and get down to concrete conclusions.
 Angles help predict how the players move, and also determine how to defend a player. Facing the
player directly will give the player greater space to move on either side. However, facing the player
at an angle will reduce their ability to move in certain directions.
Applications of Units of Angles

11.  Another example also in football, is a player passing a ball to another , where he must calculate the
angle to ensure the ball is collected by the other player.
 In Architecture, it is used to ensure that window panes, windows, and doors are proportionate and
even.
Applications of Units of Angles

12.  In basketball , you must use angles of elevation to find what angle you need to shoot at in order to
make a basket. This of course will vary between players based on their height.
 Another example, in football, the player must calculate the angle the ball must be hit in order to get
the ball past the goalkeeper and into the net.
Applications of Units of Angles

13.  Another use is in fitting certain items e.g. sofas into your home. We do not want to buy a sofa and
realize it cannot around the wall so you need angles. Also, to make sure doors do not hit objects
and walls, you need to use loci which are a type of angle.
 If we look at around us we will see angles everywhere.
Applications of Units of Angles

14. • Blank, B. A Joint Review of 1. A History of Pi, by Petr Beckmann. St. Martins’s Press, 1976, 200 pp.,
$11.95; Barnes and Noble Books, 1989, $14.95. 2. The Joy of Pi, by David Blatner. Walker & Co., 1997,
144 pp., $18.00. 3. The Nothing That Is, by Robert Kaplan. Oxford University Press, 1999, 225 pp.,
$22.00.
• Cotter, C. H. (1972). A brief history of the method of fixing by horizontal angles. The Journal of
Navigation, 25(4), 528-534.
• Drelich, J. W., Boinovich, L., Chibowski, E., Della Volpe, C., Hołysz, L., Marmur, A., & Siboni, S. (2019).
Contact angles: history of over 200 years of open questions. Surface Innovations, 8(1–2), 3-27.
• Bailey, D. H., Plouffe, S. M., Borwein, P. B., & Borwein, J. M. (1997). The quest for pi. The Mathematical
Intelligencer, 19, 50-56.
References