Question

7 multiple choice 1 point use the law of cosines. find m∠a to the nearest tenth of a degree. 78.8° 75.0° 64.4° 32.8°

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). In \(\triangle ABC\), if \(a = 6\), \(b = 10\), \(c = 11\), and we want to find \(\angle A\), the formula becomes \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 6\), \(b = 10\), \(c = 11\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

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Step3: Find the angle \(A\)

Since \(\cos A\approx0.8409\), then \(A=\cos^{-1}(0.8409)\). Using a calculator, \(A\approx32.8^{\circ}\)

Answer:

\(32.8^{\circ}\)