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In this triangle, we are given:

- An angle of \( 101.0^\circ \) (angle at the base opposite to side \( x \))
- An angle of \( 28.0^\circ \) (adjacent to the side labeled \( x \))
- The length of one side as \( 4.0 \, \text{cm} \), which is opposite the \( 28.0^\circ \) angle.

Since we know two angles and one side, we can find the missing side \( x \) by using the Sine Rule, given the triangle's structure. However, you specifically asked to use the SOHCAHTOA method, which applies primarily to right-angled triangles.

Let’s check for an approach that aligns more closely with trigonometric functions, even though the triangle isn't right-angled. 

### Solution Steps Using the Law of Sines (if non-right triangle):
The third angle can be calculated as:
\[
\text{Third angle} = 180^\circ - 101.0^\circ - 28.0^\circ = 51.0^\circ
\]

Then, applying the Law of Sines:
\[
\frac{x}{\sin(28.0^\circ)} = \frac{4.0}{\sin(51.0^\circ)}
\]

Solving for \( x \):
\[
x = \frac{4.0 \times \sin(28.0^\circ)}{\sin(51.0^\circ)}
\]

Calculating this should give the length of \( x \). Let me know if you want me to compute the exact value, or if there are further questions. 

Would you like me to proceed with calculations or explain further?

---

**Relative Questions to Explore:**

1. What is the Law of Sines, and how does it apply to non-right triangles?
2. How can we determine whether a triangle is right-angled, given certain angles?
3. When should we use SOHCAHTOA versus the Law of Sines or Cosines?
4. What is the significance of calculating all angles in a triangle?
5. How can we verify our answers in trigonometric problems?

**Tip:** For non-right triangles, the Law of Sines or Law of Cosines is more generally applicable than SOHCAHTOA.

Use the SOHCAHTOA method to find the value of x in the triangle given the angles and one side length.

Learn how to find the length of the missing side in a triangle with angles 28°, 101°, and a side length of 4 cm. This problem applies trigonometric concepts, including the Law of Sines and the angle sum property of triangles, suitable for Grades 10-12.

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