In ΔWXY, x = 43 cm, y = 53 cm and ∠W=160°. Find the length of w, to the nearest centimeter.

To find the length of side w in triangle WXY, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite side c, the following relationship holds:

c² = a² + b² - 2ab cos(γ)

In this case, we know that side x = 43 cm, side y = 53 cm, and angle W = 160°. We want to find the length of side w, which is opposite angle W. Therefore, we can plug these values into the Law of Cosines:

w² = x² + y² - 2xy cos(W) w² = (43 cm)² + (53 cm)² - 2(43 cm)(53 cm) cos(160°)

First, calculate the squares of x and y: (43 cm)² = 1849 cm² (53 cm)² = 2809 cm²

Then, calculate the cosine of angle W: cos(160°) = -0.9397

Then, substitute these values back into the equation: w² = 1849 cm² + 2809 cm² - 2(43 cm)(53 cm)(-0.9397) w² = 4658 cm² + 2(43 cm)(53 cm)(0.9397)

Finally, calculate the square root of w² to find the length of w: w = √w²

After calculating, you will find that w is approximately 74 cm.