Final answer:
The ratio representing the sine of ∠W in ΔWXY, with given side lengths, is 60/61, which is approximately 0.9836.
Step-by-step explanation:
To find the sine of ∠W in ΔWXY, where ∠Y is a right angle (90°), we must first identify the lengths of the sides of the triangle in relation to ∠W. Since WY is the side opposite to ∠W, and WX is the hypotenuse, the sine of ∠W is calculated using the ratio of the opposite side over the hypotenuse in a right-angled triangle.
The formula to find the sine of an angle in a right-angled triangle is:
sin(∠W) = opposite/hypotenuse
In this case:
sin(∠W) = length of WY / length of XW
= 60 / 61
= 0.9836 (to four decimal places)
Therefore, the ratio representing the sine of ∠W is 60/61, which approximately equals 0.9836 when calculated to four decimal places. Keep in mind that the sine function is dimensionless, therefore the ratio is simply the numerical values without any units.