To determine which equation can be used to solve for angle [tex]\( A \)[/tex], let's start by identifying the relevant components in the given problem.
We have:
- Side [tex]\( a = 2.4 \)[/tex] meters
- Side [tex]\( b = 3.2 \)[/tex] meters
- Side [tex]\( c = 4.6 \)[/tex] meters, which is the distance between the two teams
- Angle [tex]\( C = 110^\circ \)[/tex], which is the angle between the ropes where the chest is located
Using the law of sines, we have the following relationship:
[tex]\[
\frac{\sin(A)}{a} = \frac{\sin(C)}{c} \quad \text{or} \quad \frac{\sin(A)}{a} = \frac{\sin(110^\circ)}{4.6}
\][/tex]
Given that [tex]\( a = 2.4 \)[/tex] meters, we can substitute [tex]\( a \)[/tex] and [tex]\( C = 110^\circ \)[/tex] into the equation to solve for angle [tex]\( A \)[/tex]:
[tex]\[
\frac{\sin(A)}{2.4} = \frac{\sin(110^\circ)}{4.6}
\][/tex]
Therefore, the correct equation to use to solve for angle [tex]\(A\)[/tex] is:
[tex]\[
\frac{\sin(A)}{2.4} = \frac{\sin \left(110^\circ\right)}{4.6}
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{\frac{\sin (A)}{2.4}=\frac{\sin \left(110^{\circ}\right)}{4.6}}
\][/tex]
