1. Find the value of $C$ in a triangle $A B C$ with the given information. Round your answer to the nearest tenth. \[ a=7, b=6, c=5 \]

Step 1 ：We are given a triangle ABC with side lengths a = 7, b = 6, and c = 5. We are asked to find the measure of angle C.

Step 2 ：We can use the Law of Cosines to find the value of angle C. The Law of Cosines states that \(c^2 = a^2 + b^2 - 2ab\cos(C)\), where a, b, and c are the lengths of the sides of the triangle and C is the angle we are trying to find.

Step 3 ：Substituting the given values into the formula, we get \(5^2 = 7^2 + 6^2 - 2*7*6\cos(C)\).

Step 4 ：Solving for \(\cos(C)\), we get \(\cos(C) = 0.7142857142857143\).

Step 5 ：Taking the inverse cosine of both sides, we find that C = 44.4 degrees.

Step 6 ：Final Answer: The value of \(C\) in the triangle ABC is \(\boxed{44.4}\) degrees.