Life would be awesome!
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As "awesome" as the Middle Ages in fact - would you really want that sort of life? And you use the internet to tell us think it would be awe-inspiring? Try using the word "awful" instead!
Trigomometry does NOT exist as an isolated discipline. It is one of very many branches of mathematics, without which, just think - very limited science, engineering and architecture, no navigation to speak of, no frequency-analysis so no electronics and acoustics... Without the engineering we'd have nothing to generate the electricity or use it in anyway - including your computer!
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what is the application of trigonometry in your life and future carrier
Trigonometry is important in daily life for many reasons. People use patterns and symmetry in relating to objects around them. For example. trigonometry is used in decorating a home.
There are many formulae in trigonometry, not just three. So the question cannot be answered without knowing which three you mean.
Trigonometry can be used to find the heights of buildings when paired with a sextant (a device for measuring angles from the buliding)
Amongst other factors, the answer depends onwhere you took trigonometry (which country/school),what level you studied,what you want to do in life.