In the triangle below, which equation can be used to solve for \( x \)?

A triangle \( \triangle VUW \) has the side lengths \( WU \) as \( x \) feet, \( VU \) as 13 feet, the measure of angle \( V \) as 75 degrees, and the measure of angle \( U \) as 50 degrees.

A. \( x = \frac{13 \sin(50^\circ)}{\sin(75^\circ)} \)
B. \( x = \frac{13 \sin(75^\circ)}{\sin(50^\circ)} \)
C. \( x = \frac{13 \sin(55^\circ)}{\sin(75^\circ)} \)
D. \( x = \frac{13 \sin(75^\circ)}{\sin(55^\circ)} \)

To solve for x in the given triangle, we can utilize the Law of Sines, which states that for any triangle with angles A, B, and C and their opposite sides a, b, and c respectively, the following is true:

[tex]\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}.[/tex]

Given the triangle VUW:

Side WU = x feet
Side VU = 13 feet
Angle V = 75 degrees
Angle U = 50 degrees

First, we need to determine the measure of the remaining angle, Angle W:

[tex]\text{Angle W} = 180\degree - 75\degree - 50\degree = 55\degree.[/tex]

According to the Law of Sines, we have:

[tex]\frac{x}{\sin(75\degree)} = \frac{13}{\sin(50\degree)}.[/tex]

We need to isolate x. We do this by multiplying both sides of the equation by [tex]\sin(75\degree)[/tex]:

[tex]x = \frac{13 \sin(75\degree)}{\sin(50\degree)}.[/tex]