Answer:
X = 52.4°
Step-by-step explanation:
\({a}^{2} = {b}^{2} + {c}^{2} - 2bc \: CosA\)
In the diagram, X = A, therefore;
\(CosA \: = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}\)
\(Cos \: X \: = \frac{ {{5}^{2} + {10}^{2} - {8}^{2} } }{2 \times 5 \times 10}\)
\(= \frac{100 + 25 - 64}{100}\)
[tex] = \frac{61}{100} = 0.61
X = arc cos (0.61)
X = 52. 4105°
X = 52.4°
