Question

Use the image below to answer the following question:

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 5, another leg across from angle x measuring 12, and the hypotenuse measuring 13.

What relationship do the ratios of sin x° and cos y° share?
A. The ratios are both identical. (12 over 13 and 12 over 13)
B. The ratios are opposites. (negative 12 over 13 and 12 over 13)
C. The ratios are reciprocals. (12 over 13 and 13 over 12)
D. The ratios are both negative. (negative 12 over 13 and negative 13 over 12)

Answer 1

Answer:  The ratios are both identical. (Choice A)

Why does this answer work?

Well let's refer to the diagram below.

Angle x has side 12 opposite it and the hypotenuse is 13.

This means sin(x) = opposite/hypotenuse = 12/13

Also, angle y has side 12 adjacent to it, meaning,

cos(y) = adjacent/hypotenuse = 12/13

Both trig ratios result in 12/13 and we can say sin(x) = cos(y)

One last thing to notice is that x+y = 90

In other words, if x+y = 90, then sin(x) = cos(y)

Phrased a slightly different way: if x+y = 90, then sin(y) = cos(x)