To determine the relationship between the ratios of sin x° and cos y°, we can use the information provided about the right triangle.
In a right triangle:
- The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
- The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Given the triangle:
- The leg opposite angle y (y°) has a length of 12.
- The leg opposite angle x (x°) has a length of 5.
- The hypotenuse has a length of 13.
For angle x:
- \( \sin x° = \frac{\text{Opposite (to x)}}{\text{Hypotenuse}} = \frac{5}{13} \)
For angle y:
- The adjacent side to angle y is the side opposite angle x, which is 5. Hence, we can find cos y as follows:
- \( \cos y° = \frac{\text{Adjacent (to y)}}{\text{Hypotenuse}} = \frac{12}{13} \)
Now, let's compare sin x° and cos y°:
- We have \( \sin x° = \frac{5}{13} \)
- And we don't actually need to find cos y° separately for this comparison, but from the angles in a right triangle, we can deduce that \( \cos y° = \frac{\text{Adjacent (to y)}}{\text{Hypotenuse}} = \frac{12}{13} \).
However, according to the properties of trigonometric functions in a right triangle, we actually find that:
\[ \sin x° = \cos y° \]
So, the correct answer regarding the relationship between sin x and cos y is:
- The ratios are identical (five thirteenths and five thirteenths).
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