To solve this problem, we need to apply the Law of Sines, which states:
[tex]\[
\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}
\][/tex]
First, let's define the terms:
- [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are the lengths of the sides opposite to angles [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] respectively.
- [tex]\( A \)[/tex] is the angle opposite to team A's position relative to the chest.
- The known angle is [tex]\( 110^\circ \)[/tex], which we will denote as [tex]\( \angle C \)[/tex].
Given data:
- Distance between the teams: 4.6 meters (this will be opposite the [tex]\( 110^\circ \)[/tex] angle)
- Distance from Team A to the chest: 2.4 meters (this will be the side [tex]\( a \)[/tex])
- Distance from Team B to the chest: 3.2 meters
By the problem statement and the Law of Sines, we need to match the ratio involving [tex]\( \sin (A) \)[/tex] with the given sides and angles.
Among the given options, the correct way to set up the equation using the Law of Sines is to relate [tex]\( \sin A \)[/tex] and [tex]\( \sin 110^\circ \)[/tex]:
[tex]\[
\frac{\sin (A)}{a} = \frac{\sin (110^\circ)}{4.6}
\][/tex]
Here, side [tex]\( a = 2.4 \)[/tex] meters. Therefore, the equation is:
[tex]\[
\frac{\sin (A)}{2.4} = \frac{\sin (110^\circ)}{4.6}
\][/tex]
Thus, the correct equation that can be used to solve for angle [tex]\( A \)[/tex] is:
[tex]\[
\frac{\sin (A)}{2.4} = \frac{\sin (110^\circ)}{4.6}
\][/tex]
