Question

find the measure of \\( \angle a \\). round to the nearest tenth of a degree.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the angle \(A\) opposite side \(a\), \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Let \(a = 18.4\), \(b = 9.6\), \(c = 19.6\). Then \(18.4^{2}=9.6^{2}+19.6^{2}-2\times9.6\times19.6\times\cos A\).

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Step2: Find the angle \(A\)

Since \(A=\cos^{-1}(0.366)\), using a calculator, \(A\approx68.5^{\circ}\)

Answer:

\(68.5^{\circ}\)