Question

3 multiple choice 1 point use the law of cosines. find ( m angle a ) to the nearest tenth of a degree. ( 44.0^{circ} ) ( 57.9^{circ} ) ( 84.5^{circ} ) ( 52.6^{circ} )

Explanation:

Step1: Write the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). In \(\triangle ABC\), if we want to find \(\angle A\), let \(a = 14\), \(b=16\), \(c = 20\). Then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\)

Step2: Substitute the values into the formula

Substitute \(a = 14\), \(b = 16\), \(c=20\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\)

$$
LATEXBLOCK0
$$

Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(0.71875)\), using a calculator, \(A\approx44.0^{\circ}\)

Answer:

\(44.0^{\circ}\)