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

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- Unofficialllyy

- jamiebookeater

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- mathmath333

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- mathmath333

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- Unofficialllyy

I don't really understand the question. Usually the answers are in my notes and this is what my notes say
The term trigonometry comes from a Greek word meaning “triangle measuring.”
The sine of an angle within a right triangle is found by dividing the length of the opposite side by the length of the hypotenuse.
The cosine of an angle within a right triangle is found by dividing the length of the adjacent side by the length of the hypotenuse.
The tangent of an angle within a right triangle is found by dividing the length of the opposite side by the length of the adjacent side.

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- mathmath333

forget the notes ,
just try to draw to similar right triangles by scale and pencil then choose any and other than 90 degree name it \('x'\).
then find the ratio of side opposite to \('x'\) and hypotenuse in both triangles u will find the ratio is constant
and that ratio is known as \(\sin 'x'\) similarly all other trignometric ratios will be equal

- Unofficialllyy

So they relate because when you find the sine, cosine, and tangent of the similar triangles they will all be equal?

- mathmath333

yes if the angles will be equal

- Unofficialllyy

This is one of the answers for my oral quiz so I just want to make sure I understand it. Thank you for your help!

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