Final answer:
To find all possible values of ∠W in ΔVWX, use Law of Sines and set up the equation: sin(∠W) / v = sin(∠V) / w. Solve for sin(∠W) and approximate ∠W to the nearest 10th of a degree.
Step-by-step explanation:
To find all possible values of ∠W in ΔVWX, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we have w = 4.7 inches, v = 2.4 inches, and ∠V = 8°. We are trying to find ∠W.
Using the Law of Sines, we can set up the equation: sin(∠W) / v = sin(∠V) / w. Substituting the given values, we have sin(∠W) / 2.4 = sin(8°) / 4.7.
Solving for sin(∠W), we get sin(∠W) = (2.4 / 4.7) * sin(8°). Taking the arcsin of both sides, we find that ∠W ≈ 13.4° to the nearest 10th of a degree.