Question
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 use the Law of Sines to find the length of side \( c \), we start with the formula:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
In your case, you have:
- \( A = 72^\circ \)
- \( a = 1246 \, \text{mm} \)
However, we need either another angle or the length of the other side to solve for \( c \) directly using the Law of Sines, as the formula relates the sides and angles of a triangle.
Assuming that we have additional information (like angle \( B \) or side \( b \)), we can solve for side \( c \). If not, we cannot determine \( c \) without more information.
Can you provide either angle \( B \) or \( C \), or the length of another side? If only angle \( A \) and side \( a \) are given, it's impossible to find side \( c \) uniquely without knowing at least one more angle or side of the triangle.
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
In your case, you have:
- \( A = 72^\circ \)
- \( a = 1246 \, \text{mm} \)
However, we need either another angle or the length of the other side to solve for \( c \) directly using the Law of Sines, as the formula relates the sides and angles of a triangle.
Assuming that we have additional information (like angle \( B \) or side \( b \)), we can solve for side \( c \). If not, we cannot determine \( c \) without more information.
Can you provide either angle \( B \) or \( C \), or the length of another side? If only angle \( A \) and side \( a \) are given, it's impossible to find side \( c \) uniquely without knowing at least one more angle or side of the triangle.