Why I think Trigonometry is created?

After much contemplation, I have came up with a rather self-convincing postulate as to why trigonometry is invented. Note that this is just my take on the underlying idea behind trigonometry, so it may not be as accurate compared to that of a mathematician!

Trigonometry literally means "measure of triangles", specifically right angle triangles. Why right triangles? Because it is much easier to manipulate as among the three angles in a triangle, you only need to worry about two angles while the remaining one is always 90°. Trigonometry works just as well for ordinary non-right triangles (Cosine law and Sine law) as any triangle can be viewed as a combination of 2 right angle triangles.

Now, the shape of a triangle depends entirely on its internal angles, not the length of its sides. One of the three angles only changes when any two sides of the triangle change non-proportionally or not in accordance to a certain ratio (given by the value of the trigonometric function). Only when you change any two sides of a triangle (for instance, when you want to resize the triangle) according to the ratio given by the appropriate trigonometry value, then only will the shape and thus the given angle will be preserved, only this time, the triangle have a different size. Note that the third remaining side will change according to the trigonometric ratio  as a result of the proportional change of the other two sides. 

 

So, if you want to change the length of one side of the triangle without changing the angle, we will need to change another side proportionally according to the trigonometric value for that given angle; the other remaining side will follow suit changing proportionally to either of the two sides.

Let's say we have a right angle triangle with one of the angle to be 30°. If I want side A=5 units, then by using sin 30°=1/2=A/B, side B=10 units. And by using tan 30°=(surd 3)/3=A/C, side C=5(surd 3) units.

Basically, no sides of the triangle is spared from length change if you want to resize your triangle while preserving its internal angles. But you can't simply change the length of the sides however you wish. They need to be according to a given ratio. And trigonometry provides us this ratio to resize our triangle while keeping its angle and shape intact. This resizing will also help in the use of similar triangles in navigation to determine far far distances.