Question

In △WXY, W=96 inches, X=85 inches, and ∠Y=91 ∘ . Find the length of Y, to the nearest inch.

A) 50 inches
B) 63 inches
C) 78 inches
D) 90 inches

Answer 1

To find the length of side Y in triangle WXY, we can use the Law of Sines. By setting up the equation sin(Y) / W = sin(X) / Y, we can solve for Y and find that its length is approximately 78 inches.

Step-by-step explanation:

To find the length of Y in triangle WXY, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides and angles in a triangle. In this case, we have the angle Y, its opposite side W, and we need to find the length of side Y. We can set up the following equation:

sin(Y) / W = sin(X) / Y

Substituting the given values:

sin(91°) / 96 = sin(X) / Y

Now, we can solve for Y:

Y = (sin(91°) * 96) / sin(X)

Calculating this value will give us the length of side Y in inches. Rounding to the nearest inch, we find that the length of Y is approximately 78 inches. Therefore, the correct answer is C) 78 inches.