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My understanding so far.

Sine represents a ratio of two sides of an interior angle within a right angle triangle. So given the three lengths of a triangle you can find the sine of any of the 3 interior angles.

Also if you are given the actual angle of an interior angle, you can get the sine using a calculator.

Thus, I deduce from these two statements that on a right triangle any interior angle of a specific number represents a constant raio, whatever the area of the triangle.

I can visualize that in my head to a certain extent, scaling the triangles sides equally, increases the area of the triangle but not the ratio of the sides.

But I'm wondering if I'm missing anything in terms of intuition around this?

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    It is hard to tell what is being asked here. The sine is a function, so it outputs the same value every time you give it the same input. Angles in similar triangles have the same trig ratios, as those angles are the same.2011-12-14
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    @TheChaz You're right, my question is vague. One good point that you helped me clarify in your comment, was the fact that sine is a function. Being a function it can't map to multiple results from the same input. I guess I just struggled with the fact that the sine of X degree is always the same. No matter the size of the triangle. I still can't quite grasp the impact that a 90 degree triangle has on maintaining a constant ratio. For example what happens in non-90 degree triangles with sine?2011-12-14
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    Trig ratios don't have the same visible connection to sides in non-right triangles (there's a word for those - just can't remember it!). The sine of, say, the 45 degree angle in a 35-45-100 triangle would still be 1/sqrt2, but you'd have to draw altitudes to see such ratios.2011-12-14
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    Here's what I suspect is meant. Take two right triangles with the same shape but different sizes; each has a $\theta^\circ$ angle. Look at the ratio of opposite to hypontenuse. Lo and behold, it's the same in both triangles, despite the difference in sizes. So the question would be: why? How is that proved?2011-12-14
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    OBLIQUE triangles! Had to dig out a precal book... :)2011-12-14

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