Question

which equation could be used to solve for the length of side c, given a = 5, b = 12, and c = 72°? not drawn to scale c² = 5² + 12² - 2(5)(12)cos72° c² = 5² + 12² + 2(5)(12)cos72° c² = 5² - 12² - 2(5)(12)cos72° c² = 5² - 12² + 2(5)(12)cos72°

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).

Step2: Substitute the given values

Given \(a = 5\), \(b = 12\), and \(C = 72^{\circ}\). Substitute these into the formula:
\(c^{2}=5^{2}+12^{2}-2\times5\times12\times\cos72^{\circ}\)

Answer:

\(c^{2}=5^{2}+12^{2}-2(5)(12)\cos72^{\circ}\) (First option)