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To solve the given problem using the Law of Sines, we start with the information provided:

- Angle \( A = 98.4^\circ \)
- Angle \( B = 24.6^\circ \)
- Side \( a = 304 \) (opposite to angle \( A \))
- Side \( x \) is the side opposite angle \( B \).

### Step 1: Find the third angle
Since the sum of the angles in a triangle is \( 180^\circ \), we can find the third angle \( C \):

\[
C = 180^\circ - A - B = 180^\circ - 98.4^\circ - 24.6^\circ = 57^\circ.
\]

### Step 2: Apply the Law of Sines
The Law of Sines states:

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

Using \( a = 304 \), \( A = 98.4^\circ \), and \( B = 24.6^\circ \), we solve for \( x \):

\[
\frac{304}{\sin 98.4^\circ} = \frac{x}{\sin 24.6^\circ}.
\]

Simplify and solve for \( x \):

\[
x = 304 \times \frac{\sin 24.6^\circ}{\sin 98.4^\circ}.
\]

### Step 3: Calculate the values
Let’s calculate \( x \) using the given values.

\[
\sin 98.4^\circ \approx 0.9994, \quad \sin 24.6^\circ \approx 0.4166.
\]

\[
x = 304 \times \frac{0.4166}{0.9994} \approx 304 \times 0.4168 \approx 126.71.
\]

### Final Answer
\[
\boxed{x \approx 126.71}
\]

Would you like further details, or do you have any other questions?

### Related Questions:
1. How can the Law of Sines be used to find unknown angles?
2. What are other scenarios where the Law of Sines is useful?
3. How would the solution change if side \( a \) were different?
4. Can we solve this problem using the Law of Cosines?
5. How do you calculate the area of a triangle using sine?

### Tip:
Always check if the triangle is possible with given measurements using the triangle inequality before using the Law of Sines.

Use the Law of Sines to find the indicated side x. (Assume a = 304. Round your answer to two decimal places.) The triangle has angles A = 98.4°, B = 24.6°, and side a = 304 opposite angle A.

Learn how to solve for side x in a triangle using the Law of Sines with angles A = 98.4°, B = 24.6°, and side a = 304. This step-by-step solution demonstrates the use of trigonometric principles and provides a rounded answer to two decimal places.

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