To solve this triangle using the Law of Cosines, we can determine the missing side or angle if at least three pieces of information are known (two sides and the included angle or three sides).

The Law of Cosines formula is:

$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$

Given the side lengths:

• $a = 6$
• $b = 8$
• $c = 7$

We can find the angle opposite side $c$ (denoted as $\angle C$).

Using the Law of Cosines:

$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$

Let's calculate the angle $\angle C$ using these values.It seems I encountered an error. Let me correct that and calculate the angle $\angle C$ again.The angle opposite the side of length 7 (denoted as $\angle C$) is approximately $57.91^\circ$.

Would you like any further details or have any other questions?

Here are five questions you might consider asking:

1. How do you find the other angles using the Law of Cosines?
2. What are some common applications of the Law of Cosines in real-life situations?
3. How does the Law of Sines differ in application compared to the Law of Cosines?
4. Can you use the Law of Cosines for right triangles, and if so, how does it simplify?
5. How can you verify the accuracy of angle calculations in a triangle?

Tip: When using the Law of Cosines, ensure all angle measures are in the same unit (degrees or radians) to avoid calculation errors.