To use the Law of Sines in the triangle you described, we first need to identify the angles and sides. Since it is stated that \( m∠C = 38° \) and \( c = 22 \text{ mi} \) (where \( c \) is the side opposite angle \( C \)), and angle \( B \) is given as a right angle (90°), we can infer that angle \( A \) can be found using the triangle angle sum property.
Given:
- \( m∠B = 90° \)
- \( m∠C = 38° \)
- Thus, \( m∠A = 180° - m∠B - m∠C = 180° - 90° - 38° = 52° \)
Now we have:
- Angle \( A = 52° \)
- Angle \( B = 90° \)
- Angle \( C = 38° \)
- Side \( c = 22 \) mi (opposite angle \( C \))
According to the Law of Sines: \[ \frac{a}{\sin A} = \frac{c}{\sin C} \] Substituting the values we have: \[ \frac{a}{\sin 52°} = \frac{22 \text{ mi}}{\sin 38°} \]
This translates to the equation: \[ \sin 52° \cdot 22 \text{ mi} = \sin 38° \cdot a \]
Therefore, the correct choice to represent how the Law of Sines can be used to find \( a \) is: \[ \sin 38° \cdot 22 \text{ mi} = \sin 52° \cdot a \]
So the best answer among the provided options would be: \[ \sin 38° / 22 \text{ mi.} = \sin 52° / a \]
In summary, the answer that shows how the Law of Sines can be used to find \( a \) is: \[ \sin 52° / 22 \text{ mi.} = \sin 38° / a \]
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