Problem
10 Given the triangle above, choose all the possible formulas that can be used to solve the triangle. Select one or more: a. $c^{2}=a^{2}+b^{2}-2 a b \cos C$ b. $b^{2}=a^{2}+c^{2}-2 b c \cos B$ c. $c^{2}=a^{2}+b^{2}-2 b c \cos C$ d. $a^{2}=b^{2}+c^{2}-2 b \cos B$ e. $a^{2}=b^{2}+c^{2}-2 b c \cos A$ f. $b^{2}=a^{2}-c^{2}+2 a c \cos B$
Solution
Step 1 ：Identify correct formulas using the Law of Cosines: \(c^2 = a^2 + b^2 - 2ab \cos C\), \(b^2 = a^2 + c^2 - 2ac \cos B\), and \(a^2 = b^2 + c^2 - 2bc \cos A\)
Step 2 ：Compare with given options and find matches: a, b, and e
Step 3 ：\boxed{\text{Final Answer: a, b, and e}}
