What is Trigonometry and why we chose right triangles to start learning trigonometry?

1. Trigonometry and right triangles
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Duration: 3 minutes 51 seconds

The word trigonometry was derived from two greek words “trigonon” and “metron”. Trigonon means Triangle and metron means Measure. So, trigonometry is about measurements in a triangle.
Now, what kind of measurements in a triangle?
As you know, a triangle has three sides with three interior angles and we can measure the side lengths and the interior angles of a triangle. And trigonometry is about these measurements. Or to be precise, trigonometry is about relationships between side lengths and the interior angles of triangle.

Now, the question is which type of triangle is the best option to start learning trigonometry?
As you know, we have different types of triangles in maths. On the basis of lengths of sides, we have equilateral triangles in which all three sides are of equal lengths, then we have isosceles triangles in which two sides are of equal lengths and then we have scalene triangles in which all three sides are of different lengths; all three sides are unequal.
On the basis of interior angles, we have right triangles in which one interior angle is of 90 degrees, then we have acute triangles in which all three angles are smaller then 90 degrees and we have obtuse triangles in which one interior angle is greater than 90 degrees. types of triangles

Now, the classification on the basis of interior angles is quite interesting, because we can easily draw a relationship between right triangles, acute triangles and obtuse triangles, which is not quite easily possible in the case of equilateral triangles, isosceles triangles and scalene triangles.

In case of obtuse and acute triangles, if you draw perpendicular like these then you will always get two right triangles. Or in other words, you can say that acute triangles and obtuse triangles can be represented as two joined right triangles. So, the right triangles are the best option to start learning trigonometry.

traingles on the basis of interior angles

If we start learning trigonometry with right triangles then we can easily expand our rules, our concepts to other triangles; we can easily expand our rules to acute triangles and obtuse triangles, which is not possible in case of other triangles. So, right triangles are the best option.
There are some more advantages of choosing right triangles. First, the obvious one, in right triangles we already have measurement of one interior angle 90 degrees, the right angle. Which gives us the idea that other two angles are always complementary; the sum of other two angles is always 90 degrees. So, if angle A in case of right triangles is 20 degrees, then angle C will always be of 70 degrees and if angle A is of 50 degrees, then angle C will always be of 40 degrees. So, if we assume angle A as variable x degrees then angle C will always be 90 – x degrees. It means, in case of right triangles we can easily represent all interior angles by a single variable, which is not always possible in case of other triangles; which is not always possible in case of acute triangles and obtuse triangles.

Second reason is, as we have learnt in geometry that the side opposite to the largest angle is the longest side. And in case of all right triangles 90 degrees is the largest angle and side opposite to 90 degrees is always the longest side; or the hypotenuse is always the longest side in right triangles.
Which gives us the direct relationship between side length and interior angle of triangle. Which is the whole purpose of trigonometry; which is the whole base for trigonometry. That’s why right triangles are the best option to start learning trigonometry.