Question

which equation correctly applies the law of cosines to solve for an unknown angle measure? o 7² = 8² + 11² - 2(8)(11)cos(n) o 8² = 7² + 11² - 2(7)(11)cos(m) o 7² = 8² + 11² - 2(8)(11)cos(p) o 8² = 7² + 11² - 2(7)(11)cos(p) law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Recall law of cosines

$a^{2}=b^{2}+c^{2}-2bc\cos(A)$, where $a$ is the side opposite angle $A$, and $b$, $c$ are the other two - sides.

Step2: Analyze each option

For $\triangle PMN$, if we want to find an angle using the law of cosines:

• If we consider the side opposite angle $P$ has length $8$. According to the law of cosines, $8^{2}=7^{2}+11^{2}-2(7)(11)\cos(P)$.

Answer:

$8^{2}=7^{2}+11^{2}-2(7)(11)\cos(P)$