Question
Use the Law of Sines to find the length of side c, to the nearest millimeter, if ∠A=72 degrees and side a=1,246 mm .(1 point)Responses385 mm385 mm366 mm366 mm405 mm405 mm3,835 mm3,835 mm
Answers
GPT-4o mini
To find the length of side \( c \) using the Law of Sines, we can use the formula:
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
We need to know angle \( C \) in order to use this formula. However, since we do not have that information, we can assume it is either provided or will be given later. For now, let's set up the equation and calculate \( c \) based on \( A = 72^\circ \) and \( a = 1246 \, mm \).
Assuming you have another angle \( C \) (due to the lack of information about angle \( B \)), let’s denote angle \( B \) as \( \beta \), so:
\[
C = 180^\circ - (A + \beta)
\]
Now using the Law of Sines, we need to calculate it as follows. Let's rearrange the Law of Sines:
\[
c = a \cdot \frac{\sin C}{\sin A}
\]
If we know \( C \), we can plug in the values:
1. First find \( \sin A \):
\[
\sin A = \sin(72^\circ)
\]
Using the calculator:
\[
\sin(72^\circ) \approx 0.9511
\]
2. Now we can calculate \( c \) if we know \( C \). As we lack information about angle \( C \), please provide the required angle or another side or angle information to complete the calculation for \( c \).
If \( C \) is available, you would have:
\[
c = 1246 \cdot \frac{\sin C}{0.9511}
\]
With the known \( C \), you can find \( c \) and round it to the nearest millimeter.
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
We need to know angle \( C \) in order to use this formula. However, since we do not have that information, we can assume it is either provided or will be given later. For now, let's set up the equation and calculate \( c \) based on \( A = 72^\circ \) and \( a = 1246 \, mm \).
Assuming you have another angle \( C \) (due to the lack of information about angle \( B \)), let’s denote angle \( B \) as \( \beta \), so:
\[
C = 180^\circ - (A + \beta)
\]
Now using the Law of Sines, we need to calculate it as follows. Let's rearrange the Law of Sines:
\[
c = a \cdot \frac{\sin C}{\sin A}
\]
If we know \( C \), we can plug in the values:
1. First find \( \sin A \):
\[
\sin A = \sin(72^\circ)
\]
Using the calculator:
\[
\sin(72^\circ) \approx 0.9511
\]
2. Now we can calculate \( c \) if we know \( C \). As we lack information about angle \( C \), please provide the required angle or another side or angle information to complete the calculation for \( c \).
If \( C \) is available, you would have:
\[
c = 1246 \cdot \frac{\sin C}{0.9511}
\]
With the known \( C \), you can find \( c \) and round it to the nearest millimeter.