Question

In ΔWXY, where W = 96 inches, X = 85 inches, and ∠Y = 91°, find the length of side Y, to the nearest inch.

A. 96 inches
B. 85 inches
C. 124 inches
D. 43 inches

Answer 1

To find the length of side Y in triangle WXY, we can use the law of sines. The equation is sin(Y)/W = sin(X)/Y. By substituting the given values, we can solve for Y.

Step-by-step explanation:

To find the length of side 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 of a triangle to the sine of its opposite angle is constant. In this case, we have the angle Y and the opposite side W, so we can write the equation as follows:

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

Substituting the given values, we have:

sin(91°)/96 = sin(X)/Y

Using a calculator, we can find that sin(91°) is approximately 0.9986, so the equation becomes:

0.9986/96 = sin(X)/Y

Solving for Y, we get:

Y ≈ (96 * sin(X)) / 0.9986

Now, let's calculate the value of sin(X) using the law of cosines:

cos(X) = (W² + X² - Y²) / (2W * X)

Substituting the given values:

cos(X) = (96² + 85² - Y²) / (2 * 96 * 85)

Using a calculator, we can find that cos(X) is approximately 0.3655. Taking the inverse cosine of this value, we get:

X ≈ cos⁻¹(0.3655)

Now we can substitute the value of X into the equation for Y to find the approximate length of side Y:

Y ≈ (96 * sin(X)) / 0.9986