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How do similar right triangles lead to the definitions of the trigonometric ratios?

@jim_thompson5910 Could you try to help?

let's say we had this right triangle
|dw:1433986107369:dw|

Alright

cut each length in half to get this similar triangle
|dw:1433986215952:dw|

oops typo
|dw:1433986258148:dw|

let's say we place the reference angle theta here
|dw:1433986304712:dw|

the ratio of those two sides forms the sine of the angle theta

|dw:1433986433430:dw|

you agree that similar right triangles have the same angles right?

Yes

Ummm using AAA or the other ones lol

but we know nothing about the angles

let's say you had only a ruler

using the ruler, you can measure the segments but not the angles

Right

So how do similar right triangles and the trig ratios relate? I don't get it

Oh so the trigonometric ratios will always be the same with similar right triangles

|dw:1433987739690:dw|

the sides may change, but their relationship or ratio will stay the same