Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share? A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 12, another leg across from angle x measuring 5, and the hypotenuse measuring 13. The ratios are opposites (negative five thirteenths and five thirteenths). The ratios are both identical (five thirteenths and five thirteenths). The ratios are reciprocals (five thirteenths and thirteen fifths). The ratios are both negative (negative thirteen fifths and negative thirteen fifths).

The relationship shared by the ratios of sin x and cos y is the ratios are both identical:

We would need to apply the trigonometric ratios to find the relationship between sin x and cos y.

Recall: SOH CAH TOA

SOH represents , which is applied when the opposite side length to the reference angle and the hypotenuse length are known.

CAH represents , which is applied when the adjacent side length to the reference angle and the hypotenuse length are known.

TOA represents , which is applied when the opposite side length to the reference angle and the adjacent length are known.

*See image of the problem given in the attachment below

To find sin x, apply SOH:

Substitute:

To find cos y, apply SOH:

sin x = cos y

Therefore, the relationship between the ratios of sin x and cos y is:

The ratios are both identical:

Learn more about trigonometric ratios here:

47 - 90 = 43

43 - 180 = x

x = 137