Question
USE THE LAW OF SINES
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.
a. 405 mm
b. 3,835 mm
c. 385 mm
d. 366 mm
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.
a. 405 mm
b. 3,835 mm
c. 385 mm
d. 366 mm
Answers
GPT-4o mini
To find the length of side \( c \) using the Law of Sines, we start with the formula:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Given that \( A = 72^\circ \) and side \( a = 1246 \) mm, we need more information to find side \( c \) directly. However, we can express \( c \) in terms of another angle and side if we had either angle \( B \) or \( C \).
Without loss of generality, let's denote the other angles as \( B \) and \( C \).
Since we do not have \( B \) or \( C \), we can find the relationship needed to compute side \( c \), knowing \( \sin A \) and using the Law of Sines.
1. Calculate \( \sin A \):
\[
\sin A = \sin(72^\circ) \approx 0.9511
\]
2. Now, using the Law of Sines:
\[
\frac{c}{\sin C} = \frac{1246}{0.9511}
\]
3. To solve for \( c \), we need \( \sin C \):
However, we notice we need either \( B \) or \( C \) or additional parameters to proceed.
Due to the lack of additional angles or sides in the problem statement, we cannot find an exact numerical answer for \( c \) without making assumptions or receiving further information. Please provide the missing angles or additional information about triangle characteristics if available. If we assume some angles, we could calculate \( c \) based on those angles, but we need that explicit information.
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Given that \( A = 72^\circ \) and side \( a = 1246 \) mm, we need more information to find side \( c \) directly. However, we can express \( c \) in terms of another angle and side if we had either angle \( B \) or \( C \).
Without loss of generality, let's denote the other angles as \( B \) and \( C \).
Since we do not have \( B \) or \( C \), we can find the relationship needed to compute side \( c \), knowing \( \sin A \) and using the Law of Sines.
1. Calculate \( \sin A \):
\[
\sin A = \sin(72^\circ) \approx 0.9511
\]
2. Now, using the Law of Sines:
\[
\frac{c}{\sin C} = \frac{1246}{0.9511}
\]
3. To solve for \( c \), we need \( \sin C \):
However, we notice we need either \( B \) or \( C \) or additional parameters to proceed.
Due to the lack of additional angles or sides in the problem statement, we cannot find an exact numerical answer for \( c \) without making assumptions or receiving further information. Please provide the missing angles or additional information about triangle characteristics if available. If we assume some angles, we could calculate \( c \) based on those angles, but we need that explicit information.