The diagram you provided shows a right-angled triangle $PQR$ with $\angle Q = 90^\circ$, and a smaller right-angled triangle $PQS$, where $S$ is a point on $PR$.

From the diagram:

• $PQ = 6 \, \text{cm}$
• $QR = 3 \, \text{cm}$
• We need to find $x$, the length of segment $QS$.

To solve this, we can apply a combination of trigonometric properties and geometric principles.

Would you like me to guide you through solving this step by step?

Also, here are 5 related questions you might consider:

1. What is the Pythagorean theorem and how is it applied in right-angled triangles?
2. How can trigonometric ratios like sine, cosine, and tangent help in solving for unknown sides?
3. What is the relationship between the two right triangles in the diagram?
4. Can the length of $PR$ be found using the Pythagorean theorem?
5. How would the angle $x$ affect the overall dimensions of the triangle?

Tip: When working with right-angled triangles, always check if the Pythagorean theorem or trigonometric ratios apply, especially for problems involving unknown lengths.