Question

find ( mangle x ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle x=square^{circ} )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle WXY\), let \(a = 12\), \(b = 10\), \(c = 7\), and \(C=\angle X\). Then \(7^{2}=12^{2}+10^{2}-2\times12\times10\times\cos\angle X\).

Step2: Simplify the equation

$$
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$$

Step3: Find the angle

\(\angle X=\cos^{-1}(\frac{13}{16})\). Using a calculator, \(\cos^{-1}(\frac{13}{16})\approx35.3^{\circ}\)

Answer:

\(35.3\)