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'll start with the given information:

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

The Law of Sines states that:

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

We only have information about \( \angle C \) and side \( c \). To find side \( a \), we also need the measure of \( \angle A \) or \( \angle B \). Without additional information about the other angles or side lengths, we cannot directly find side \( a \).

If we assume that we have another angle (say, \( \angle A \)), we could proceed with the calculations as follows:

1. Calculate \( \sin C \):

\[
\sin 28^\circ \approx 0.4695
\]

2. Set up the ratio using the Law of Sines:

\[
\frac{a}{\sin A} = \frac{28}{\sin 28^\circ}
\]

3. From this, we get:

\[
a = \frac{28 \cdot \sin A}{\sin 28^\circ}
\]

4. Substituting the value of \( \sin 28^\circ \):

\[
a = \frac{28 \cdot \sin A}{0.4695}
\]

5. To find \( a \), we'll need the value of \( \sin A \).

If you provide the value for either \( \angle A \) or \( \angle B \), then we can find \( a \). Otherwise, additional details are needed to give a specific numerical answer for side \( a \).

Please provide any missing information, or let me know how you would like to proceed!