It seems that the problem involves a triangle where we are tasked to find the length of side $CD$. Here's a breakdown based on the image:

• $AB = 6 \, \text{cm}$
• $AC = 12 \, \text{cm}$
• $\angle DAB = 55^\circ$
• We need to calculate the length of $CD$ to 3 significant figures.

Steps to Solve:

1. Use the Law of Cosines: Since we have the angle between two known sides $AB$ and $AC$, we can apply the law of cosines: $CD^2 = AB^2 + AC^2 - 2 \cdot AB \cdot AC \cdot \cos(\angle DAB)$
2. Substitute the values: $CD^2 = 6^2 + 12^2 - 2 \cdot 6 \cdot 12 \cdot \cos(55^\circ)$
3. Simplify the equation and solve for $CD$.

Let me calculate this for you.The length of $CD$ is approximately $9.87 \, \text{cm}$ when rounded to 3 significant figures.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does the law of cosines relate to the Pythagorean theorem?
2. What happens when the angle in the law of cosines is $90^\circ$?
3. Can you apply the law of sines to this triangle? If so, how?
4. How can we solve a triangle when we know only two angles and one side?
5. What is the significance of using radians in trigonometric calculations?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) based on the angle units you're working with.