Question

explain how the three trig functions can be found by creating a ratio of the side lengths in a right triangle? What are the three trig functions?How can they be written as a ratio of the sides?

Answer 1

Three trigonometric functions are sinФ, cosФ, tanФ

For the shown right triangle ABC, AB is side opposite to angle Ф, BC is side adjacent to angle Ф and side AC is hypotenuse side( side opposite right angle)

All three trigonometioc ratios can be found from sides of triangle by

formulas as written

SinФ =
`(opposite-side)/(hypotenuse ) = (AB)/(AC)`

cosФ =
`(adjacent-side)/(hypotenuse) = (BC)/(AC)`

tanФ =
`(opposite-side)/(ajacent-side) = (AB)/(BC)`