Use the image below to answer the following question. find the value of sin x° and cos y°. what relationship do the ratios sin x° and cos y° share?

sin(x)=cos(y) by the co-function identity.

step-by-step explanation:

i'm going to use soh cah toa for this.

this means sine is opposite over hypotenuse and cosine is adjacent over hypotenuse. the tangent is opposite over adjacent. it looks like we don't need that ratio for this problem.

looking at the triangle from x's point of view: i see that the side with 8 measurement is opposite (not touching our angle) while the side measuring 15 units is adjacent to.   the hypotenuse is the same from any point of view, let's cat it h.

therefore, sin(x)=8/h .

looking at the triangle from y's point of view: i see that the side measuring 15 is opposite to angle y and that the side measuring 8 is adjacent to.   again we are still using that the hypotenuse is h units long.

cos(y)=8/h.

you should see here that cos(y)=sin(x) since they both have the same ratio,8/h.

by the way we could have used pythagorean theorem to find h, but it wasn't necessary.

anyways y is equal to 90-x because the angles of a triangle must add up to be 180.

so sin(x)=cos(y) by the co-function identity.