Question

Question was provided via image upload.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for a triangle with sides \(a\), \(b\), \(c\) and the angle \(x\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos x\). Here, \(a = 10\), \(b = 14\), \(c = 12\). So, \(12^{2}=10^{2}+14^{2}-2\times10\times14\times\cos x\).

Step2: Simplify the equation

$$
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$$

Step3: Solve for \(\cos x\)

\(\cos x=\frac{152}{280}=\frac{19}{35}\approx0.5429\)

Step4: Find the value of \(x\)

\(x=\cos^{- 1}(\frac{19}{35})\approx57.1^{\circ}\)

Answer:

\(x\approx57.1^{\circ}\)