Question
in the triangle shown, mC = 38" and c = 22 mi. Which equation shows how the Law of Sines can be used to find a?
(1 point)
(1 point)
Answers
GPT-4o mini
To use the Law of Sines to find side \( a \) in the triangle where \( mC = 38^\circ \) and \( c = 22 \) mi, we can apply the following formula from the Law of Sines:
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
In this equation, \( A \) is the angle opposite side \( a \), \( C \) is the angle opposite side \( c \), and \( a \) and \( c \) are the lengths of the sides opposite those angles, respectively.
Since you are looking for the equation to find \( a \), you can rearrange the equation as follows:
\[
a = \frac{c \cdot \sin A}{\sin C}
\]
Substituting the known values into the formula will allow you to find \( a \) once you know angle \( A \).
To summarize, the correct equation using the Law of Sines to find \( a \) is:
\[
a = \frac{22 \cdot \sin A}{\sin 38^\circ}
\]
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
In this equation, \( A \) is the angle opposite side \( a \), \( C \) is the angle opposite side \( c \), and \( a \) and \( c \) are the lengths of the sides opposite those angles, respectively.
Since you are looking for the equation to find \( a \), you can rearrange the equation as follows:
\[
a = \frac{c \cdot \sin A}{\sin C}
\]
Substituting the known values into the formula will allow you to find \( a \) once you know angle \( A \).
To summarize, the correct equation using the Law of Sines to find \( a \) is:
\[
a = \frac{22 \cdot \sin A}{\sin 38^\circ}
\]