To solve for angle [tex]\( A \)[/tex] using the Law of Sines, we can follow these steps:
1. Identify the given values:
- Distance from Team A to the chest ([tex]\(a\)[/tex]): [tex]\(2.4\)[/tex] meters
- Distance from Team B to the chest ([tex]\(b\)[/tex]): [tex]\(3.2\)[/tex] meters
- Distance between the teams ([tex]\(c\)[/tex]): [tex]\(4.6\)[/tex] meters
- Angle opposite to side [tex]\(c\)[/tex]: [tex]\(\angle C = 110^\circ\)[/tex]
2. Write the Law of Sines formula:
The Law of Sines states that:
[tex]\[
\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}
\][/tex]
3. Substitute the given values into the Law of Sines:
We need to find an equation that helps us solve for angle [tex]\( A \)[/tex]. Given the side [tex]\(a\)[/tex] and the angle [tex]\(C\)[/tex] opposite to side [tex]\(c\)[/tex], we get:
[tex]\[
\frac{\sin (A)}{2.4} = \frac{\sin (110^\circ)}{4.6}
\][/tex]
4. Conclude with the correct equation:
The correct equation to use for solving angle [tex]\( A \)[/tex] is:
[tex]\[
\frac{\sin (A)}{2.4} = \frac{\sin (110^\circ)}{4.6}
\][/tex]
Therefore, the equation that can be used to solve for angle [tex]\( A \)[/tex] is:
[tex]\[
\boxed{\frac{\sin (A)}{2.4} = \frac{\sin (110^\circ)}{4.6}}
\][/tex]
