Question
In the triangle shown, m∠e C=38° and c=22mi. Which equation shows how the Law of Sines can be used to find a?
Answers
GPT-4o mini
To use the Law of Sines in a triangle where you know one angle and its opposite side, you can set it up with the following relation:
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
In your case, you've provided \( m\angle C = 38^\circ \) and \( c = 22 \, \text{mi} \).
To find \( a \), we can rearrange the Law of Sines equation like this:
\[
a = \frac{c \cdot \sin A}{\sin C}
\]
Substituting the known values:
\[
a = \frac{22 \, \text{mi} \cdot \sin A}{\sin(38^\circ)}
\]
This equation shows how you can use the Law of Sines to find side \( a \) when you know side \( c \) and angle \( C \), and also need angle \( A \). Note that you'll need to find angle \( A \) using the triangle angle sum property if it hasn't been provided.
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
In your case, you've provided \( m\angle C = 38^\circ \) and \( c = 22 \, \text{mi} \).
To find \( a \), we can rearrange the Law of Sines equation like this:
\[
a = \frac{c \cdot \sin A}{\sin C}
\]
Substituting the known values:
\[
a = \frac{22 \, \text{mi} \cdot \sin A}{\sin(38^\circ)}
\]
This equation shows how you can use the Law of Sines to find side \( a \) when you know side \( c \) and angle \( C \), and also need angle \( A \). Note that you'll need to find angle \( A \) using the triangle angle sum property if it hasn't been provided.