It is used to calculate the trajectories of projectiles and missiles.
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Plane trigonometry is trigonometry carried out in (on) a plane. This could be contrasted with spherical trigonometry, which is trigonometry carried out on the surface of a sphere. Certainly there are some other more complex forms of trig.
With a protractor. Or measure some distance, and use trigonometry.
In general, you measure it. In a few special cases you may be able to use geometry or trigonometry.
Trigonometry
The way you do trigonometry is by working with triangles. Trigonometry is a math class that is taught in high school and usually followers algebra and geometry.