Applications and Models
Applications involving right triangles
The three angles of a right triangle are denoted by the letters A, B, and C (where C is the right angle), and the lengths of the sides opposite to these angles by the letters a, b, and c (where c is the hypotenuse).
Angles of elevation and depression
In surveying, the angle of elevation is the angle from the horizontal looking up to some object.
The angle of depression is the angle from the horizontal looking down to some object.
Application involving Bearings
In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line sight makes with a fixed north – south line.
There are two methods for expressing bearing.
- Single Angle Given: When a single angle is given, it is understood that the bearing is measured in a clockwise direction from due north. In general in air navigation, bearings are measured in degrees clockwise from north.
- The second method starts with a north-south line and uses an acute angle to show the direction, either east or west, from this line.
Find out more about right triangles, directional bearings, and harmonic motion below.
Practice: Solve problems involving right triangles, directional bearings, and harmonic motion in the following exercises.