The problem you provided shows a triangular piece of land with two known side lengths $A = 80 \, \text{m}$, $B = 95 \, \text{m}$, and two angles $\theta$ and the interior angles of $11^\circ$ and $21^\circ$. The question asks to find the third side $C$ and the angle $\theta$.

To solve this, we can use the Law of Cosines to find the unknown side $C$:

$C^2 = A^2 + B^2 - 2AB \cdot \cos(\theta)$

But first, we need to calculate $\theta$. Since the total sum of angles in a triangle is $180^\circ$, we can find $\theta$ as:

$\theta = 180^\circ - 11^\circ - 21^\circ = 148^\circ$

Now, we can apply the Law of Cosines to solve for $C$.

Let me calculate that for you.The length of the third side $C$ is approximately $168.27 \, \text{m}$.

Do you want further details or have any other questions?

Here are some related questions to expand your understanding:

1. How is the Law of Cosines used in more complex geometries?
2. Can the Law of Sines be used to find unknown angles and sides in this case?
3. How do different methods of solving triangles compare in terms of complexity and applicability?
4. What other real-life applications use the Law of Cosines for non-right triangles?
5. How does angle measurement accuracy affect the outcome of triangular calculations?

Tip: Always ensure your calculator is in the correct mode (degrees/radians) when solving trigonometric functions based on the angle unit given in the problem.