Question

10.2 use law of cosines to
10 multiple choice 1 point
use the law of cosines. find ( m angle a ) to the nearest tenth of a degree.
examples:

1. find ( m angle c )

( 7 ^ { 2 } = 11 ^ { 2 } + 6 ^ { 2 } - 2 ( 11 ) ( 6 ) cos c )

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a\), \(b\), \(c\) are the sides of the triangle and \(C\) is the angle opposite to side \(c\). In \(\triangle ABC\), if we want to find \(\angle A\), let \(a = 7\), \(b = 18\), \(c = 16\). Then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 7\), \(b = 18\), \(c = 16\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

$$
LATEXBLOCK0
$$

Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(0.921875)\), using a calculator, \(A\approx22.8^{\circ}\)

Answer:

\(22.8^{\circ}\)