To solve the problem using the Law of Sines, let's first identify the given distances in the context of a triangle formed by the points where the ropes are attached and the chest.
1. The distance between Team A and Team B ([tex]\(AB\)[/tex]) is 4.6 meters.
2. The distance from Team A to the chest ([tex]\(AX\)[/tex]) is 2.4 meters.
3. The distance from Team B to the chest ([tex]\(BX\)[/tex]) is 3.2 meters.
4. The angle between the teams' ropes is [tex]\(110^\circ\)[/tex].
We will use the Law of Sines which states:
[tex]\[
\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}.
\][/tex]
In our case, angle [tex]\(C\)[/tex] is [tex]\(110^\circ\)[/tex]. We need to set up an equation to find angle [tex]\(A\)[/tex], which is the angle opposite to side [tex]\(AX\)[/tex] (2.4 meters).
To use the Law of Sines:
[tex]\[
\frac{\sin(A)}{AX} = \frac{\sin(C)}{AB}
\][/tex]
Substitute the known values into the equation:
[tex]\[
\frac{\sin(A)}{2.4} = \frac{\sin(110^\circ)}{4.6}.
\][/tex]
Therefore, the correct equation to solve for angle [tex]\(A\)[/tex] using the Law of Sines is:
[tex]\[
\frac{\sin(A)}{2.4}=\frac{\sin \left(110^{\circ}\right)}{4.6}.
\][/tex]
