Question

use the law of sines to solve the following problem. if C = 28 degrees and side c = 28 m, then what is the length of side a to the nearest meter

Answer 1

To solve for side \( a \) using the Law of Sines, we can apply the formula:

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

Given:
- \( C = 28^\circ \)
- \( c = 28 \, \text{m} \)

However, we don't have angles \( A \) and \( B \) yet, so we need more information to find side \( a \). Let's proceed with some assumptions to demonstrate how to find \( a \).

Assuming we need angle \( A \) to find side \( a \). Rearranging the Law of Sines gives:

\[
a = \frac{c \cdot \sin(A)}{\sin(C)}
\]

To calculate \( a \), we need either \( A \) or \( B \). If we assume we have angle \( A \), we can substitute \( A \) into the equation above.

Let's say angle \( A \) is something specific; for demonstration purposes, let's assume \( A = 40^\circ \):

Now applying our values, we can calculate:

\[
\frac{a}{\sin(40^\circ)} = \frac{28}{\sin(28^\circ)}
\]

First, calculate \( \sin(28^\circ) \) and \( \sin(40^\circ) \):

- \( \sin(28^\circ) \approx 0.4695 \)
- \( \sin(40^\circ) \approx 0.6428 \)

Now we can plug these into the Law of Sines equation:

\[
\frac{a}{0.6428} = \frac{28}{0.4695}
\]

Calculating the right hand side:

\[
\frac{28}{0.4695} \approx 59.7
\]

Now, we set up the equation:

\[
\frac{a}{0.6428} = 59.7
\]

Solving for \( a \):

\[
a = 59.7 \cdot 0.6428 = 38.34
\]

Rounding to the nearest meter, \( a \approx 38 \, \text{m} \).

However, please note that the final answer will be dependent on the value of \( A \) or another angle or side provided.