Final answer:
Using the Law of Sines in triangle AUVW, with side U=44 inches and angles W=56° and U=117°, we find that side v is approximately 30 inches.
Step-by-step explanation:
To solve for the length of side v in triangle AUVW, we will 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 sides and angles in a triangle.
Given: U = 44 inches, ∠W = 56°, and ∠U = 117°. To find side v, we first need the measure of angle V. Since the sum of the angles in any triangle is 180°, we can find angle V: ∠V = 180° - ∠W - ∠U = 180° - 56° - 117° = 7°.
Then we apply the Law of Sines:
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- sin(∠W) / w = sin(∠U) / u = sin(∠V) / v
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- sin(56°) / w = sin(117°) / 44
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- v = (44 * sin(56°)) / sin(117°)
After calculating, we find that v is approximately 30 inches, which corresponds to option A.