Question

fall 2025 geometry b wwva right triangle relationships and trigonometry which equation correctly applies the law of cosines to solve for an unknown angle measure? 7² = 8² + 11² - 2(8)(11)cos(p) 8² = 7² + 11² - 2(7)(11)cos(m) 7² = 8² + 11² - 2(8)(11)cos(n)

Explanation:

Step1: Recall law of cosines

The law of cosines for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos(\theta)\).

Step2: Identify sides and angle

In \(\triangle PMN\), if we want to find an angle - say the angle opposite to side \(MN = 7\), let \(a = 8\), \(b = 11\) and \(c = 7\). The angle opposite to side \(c\) is \(\angle P\).

Step3: Apply law of cosines

Substituting into the law - of - cosines formula, we get \(7^{2}=8^{2}+11^{2}-2(8)(11)\cos(P)\).

Answer:

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