Question

use the law of cosines. find m∠a to the nearest tenth of a degree.
83.8°
56.6°
76.8°
20.4°

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). In \(\triangle ABC\), if \(BC = a = 10\), \(AC = b = 24\), \(AB=c = 28\), then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 10\), \(b = 24\), \(c = 28\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

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Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(\frac{15}{16})\), using a calculator, \(A\approx20.4^{\circ}\)

Answer:

\(20.4^{\circ}\)