The three basic ratio of relating different length are "sine", "cosine" and "tangent".
1) sine (angle) = length of opposite side / length of hypothenus
2) cosine (angle) = length of adjacent side / length of hypothenus
3) tangent (angle) = length of opposite side / length of adjacent side
The ratio of the trigonometry function is just a number! (Nothing more, nothing less).
However, this number (ratio) represents the magnitude of the angle.
Given the relevant lengths of the sides an object, the angles within can be easily found, and vice versa.
These trigonometry operations can be expanded further to double angles and trigonometric addition and subtraction.
Its application is heavily dealt with in electronics and communciation engineering, where the signals are transparent to the naked eyes. TTo model this transparent signal, trigonometric expressions are used. These signals are can be described by the Fourier Series analysis which make use of trigonometric functions.
Studies of wave motion and lately, digital and audio compression , are also examples of trigonometry usages.
Studies of optical engineering also uses trigonometry to analyze light path penetration through glass. The incidence angles where the light path enters, and ite reflection, can be obtained throught the use of trigonometric functions.
More example of trigonometrical application is in civil engineering where it is used in determining height of buildings, terrain, hills, trees, etc.
Other examples of real life applications are in land and marine navigation where the locations of vehicles has to be determined or computed.
Thus, from the few examples quoted above, it can be seen that trigonometry is a useful area within the mathematics learning context.
:) Interesting? Must be!