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)
Responses

405 mm
405 mm

3,835 mm
3,835 mm

366 mm
366 mm

385 mm

Answer 1

To use the Law of Sines to find the length of side \( c \), we first need to know the value of the angle \( C \). However, since angle \( C \) is not given, we can't directly solve for side \( c \) using only the information provided. The Law of Sines states:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

Given that we have \( A = 72^\circ \) and \( a = 1,246 \, \text{mm} \), we need to find either angle \( B \) or angle \( C \) to proceed.

If we assume that we have angle \( B \), then we can use the Law of Sines to find side \( c \). Assuming you have angle \( B \), the calculations would follow these steps:

1. Use the Law of Sines ratio to find side \( c \):
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
2. Solve for \( c \):
\[
c = a \cdot \frac{\sin C}{\sin A}
\]

Without knowing either angle \( B \) or \( C \), we cannot accurately calculate the length of side \( c \).

If you can provide angle \( B \) or \( C \), I would be happy to help you calculate the length of side \( c \). Please let me know!