trigonometry – why study triangles

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We study trigonometry because it is useful. Its earliest and simplest use is to find the missing part of a triangle. But mathematicians do not just study something because it is useful. More often, they study something because it is fascinating. What is so special about triangles? Why did mathematicians created a branch of mathematics devoted to the study of it? Why not quadrinometry? Quadrilaterals, by its variety are far more interesting. Not only that, each piece of shape is related to another piece. If you know one, you’ll know about the rest. This is precisely the reason why we study trigonometry, why we study triangles. If you know it, you’ll know about any polygon not just quadrilaterals. Any polygon can be dissected into pieces of triangles! Try dissecting any of these shapes:

There are different kinds or shapes of triangles. In terms of angles we have equiangular, acute, obtuse, and right triangles.

Why is it that we devote so much time studying about right triangles in trigonometry? Try dissecting the other triangles and you’ll know why if you know about right triangles, you’ll know about the other triangles!.

Here’s a bonus reason: when you study triangles, you don’t need to deal with nonconvex ones! 

Click here for a sample lesson on teaching trigonometry through problem solving.

2 Responses to trigonometry – why study triangles

  1. shana donohue says:

    If I give s simple tri gproblem where one angle (other than the right angle) and one side are known, they obviously have to use trig to find one of the other sides.

    But do you think it’s overkill to use a trig ratio to find the third side or to just use a2 + b2 + c2?

    In any case, I made a silly trig video that I put on YouTube.

    I use a2 + b2 = c2 to find the last side but I feel guilty that it’s not a trig video through and through! But is it overkill?

    • erlines says:

      I think P.T is as trig as it is as geometric and as algebraic concept. I think it’s best to call your video ‘solving triangle video’ rather than the more general trig video.

      I think the best is to present in the video that while the first two sides can be solved by ideas of trig ratio (actually there are other ways, e.g constructing similar triangles then use ratio and proportion or by scale drawing) the third side can be solved by trig and by P.T. I would consider it an overkill if students will be required to always use these two to solve the third side. They should know that both works. So when should they use this solution? I think that depends on the given number and the available calculator. The more keys needed to solve the problem, the greater the probability of getting incorrect answer.

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