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To solve for the value of \( x \) in the triangle using the Sine Theorem, we can follow these steps:

### Sine Theorem (Law of Sines):
The Sine Theorem states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
where \( a \), \( b \), and \( c \) are the sides of the triangle, and \( A \), \( B \), and \( C \) are the opposite angles, respectively.

### Given Information:
- \( \angle A = 60^\circ \)
- \( \angle B = 18^\circ \)
- Side \( c = 15 \) m (opposite to \( \angle B \))
- Side \( a = x \) (opposite to \( \angle A \))

### Find:
The value of \( x \).

### Steps:

1. **Find the remaining angle \( \angle C \):**
   Since the sum of the angles in a triangle is \( 180^\circ \),
   \[
   \angle C = 180^\circ - 60^\circ - 18^\circ = 102^\circ
   \]

2. **Apply the Sine Theorem:**
   \[
   \frac{x}{\sin 60^\circ} = \frac{15}{\sin 18^\circ}
   \]

3. **Solve for \( x \):**
   \[
   x = \frac{15 \times \sin 60^\circ}{\sin 18^\circ}
   \]

4. **Calculate the Sine Values:**
   - \( \sin 60^\circ \approx 0.866 \)
   - \( \sin 18^\circ \approx 0.309 \)

   So,
   \[
   x = \frac{15 \times 0.866}{0.309} \approx \frac{12.99}{0.309} \approx 42.05 \text{ m}
   \]

Thus, the value of \( x \) is approximately \( 42.05 \) meters.

Would you like further details or have any questions?

### Relative Questions:
1. How does the Law of Sines apply to non-right triangles?
2. Can the Law of Sines be used in all types of triangles? Why or why not?
3. What would happen if two angles were unknown in a triangle?
4. How does the Law of Sines differ from the Law of Cosines?
5. What are the possible limitations of using the Sine Theorem?

### Tip:
Always ensure the angles are correctly summed to \( 180^\circ \) when using the Sine Theorem in a triangle.

Learn how to find the value of x in a triangle using the Sine Theorem. This problem involves calculating side lengths and angles in a triangle using the Law of Sines. Suitable for high school students studying geometry and trigonometry.

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