What are the some applications of trigonometry?

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Wilson2014 | eNotes Employee

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Trigonometry describes the relationship between the angle of the sides or the sides themselves of a trigonal shape. These relationships can be applied in calculating the distance of objects, the angles of a trigonal system, and other naturally occuring systems. Many systems of nature can be described by these trigonometric relationships. For example, trigonometry allows us to be able to calculate the movement of waves, the time the sun sets, the path of comets, the quality of sounds, the changing rate of a shadow, etc. In general, math describes the relationships of naturally occurring phenomena. It is the language of mother nature. Trigonometry is just one portion of math that describes a certain aspect of nature; therefore, allowing us to predict the result of these naturally occuring phenomena. 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should think at law of sines or law of cosines that helps you to evaluate the measure of an angle or the length of a side not only in a right angle triangle, but in any triangle, acute or obtuse.

Hence, using the law of sines, you may write the following ratios, such that:

`a/(sin A) = b/(sinB) = c/(sin C)`

a represents the length of the side, opposed to angle `hatA`

b represents the length of the side, opposed to angle `hatB`

c represents the length of the side, opposed to angle `hatC`

Using the law of cosines, you may write the following equations that relates the squares of lengths of sides and the measure of an included angle, such that:

`a^2 = b^2 + c^2 - 2ab*cosA`

`b^2 = a^2 + c^2 - 2ac*cosB`

`c^2 =a^2 + b^2 - 2ab*cos C`

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pramodpandey | College Teacher | (Level 3) Valedictorian

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Measuring the height and distance, such as that of a triangle .