Hello!

Question

Explain why the primary trigonometric ratios depend only on the given angle and not the size of legs and hypotenuse of a right triangle?

I am not 100% sure but it is because the angles have the same value for all of the ratios? Is it also because the side lengths increase/decrease proportionally as the size of triangle changes?

Thanks!

Answer 1

You should remember that two similar triangles have their corresponding angles equal, and their corresponding sides are in the same ratio

So if, for example, you have 2 right angled triangles, one of sides 3-4-5 and the other 6-8-10
the angles would be the same
so if we let their base angles be Ø in the first ..
sinØ = 4/5 and in the second sinØ = 8/10
but 8/10 = 4/5
so the ratio defined by sine stays constant
The same is true for the cosine and the tangent ratios.

your assumption is correct

Answer 2

Thanks! :)