What are the relationships between an angle (in a triangle) and it's opposite side (in a triangle)? Does an angle determine the length of it's opposite side (in a triangle)? Are the answers to these questions the answer to why trigonometry even works? Is this why it works? Is this why trigonometry even exists? I know, this is a very BIG question and it definitely requires much critical thinking, research, effort, and time in order to answer such a broad question. So, I won't mind if nobody bothers to answer this question; I am a very curious person, and I am very eager to learn the accurate answer to the questions.
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We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles.
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