Question

first, complete the equation. c² = a² + b² - 2abcosc ?² = 4² + ² - 2(4)( )cosc enter the side length that belongs in the green box.

Explanation:

Step1: Identify the sides in the law - of - cosines formula

In the law - of - cosines formula \(c^{2}=a^{2}+b^{2}-2ab\cos C\), for a triangle with side lengths \(a = 4\), \(b = 7\), and the side opposite angle \(C\) being the unknown side we are relating to the formula.

Step2: Substitute the values into the formula

We know that the side opposite angle \(C\) is the side with length \(9\). So, when substituting \(a = 4\), \(b = 7\) into the formula \(c^{2}=a^{2}+b^{2}-2ab\cos C\), we get \([9]^{2}=4^{2}+[7]^{2}-2(4)([7])\cos C\).

Answer:

9