Final answer:
The law of cosines is applied to solve for an unknown angle by correctly arranging the sides and the angle in the formula. The correct use would have the squared length of the side opposite the angle on one side of the equation, and the sum of the squares of the other sides minus twice the product of those sides and the cosine of the unknown angle. The correct formula from the given options is 8² = 7² + 11² - 2(7)(11)cos(M), representing the angle opposite the side with length 8.
Step-by-step explanation:
The equation that correctly applies the law of cosines to solve for an unknown angle measure is the one where the known sides and the angle opposite to the unknown side are correctly placed according to the formula. Given the formula c² = a² + b² - 2ab cos y, 'c' is the side opposite to the angle 'y' we are trying to find, and 'a' and 'b' are the other two sides of the triangle.
So, using the law of cosines, if we want to find the angle 'N' that is opposite the side with length 7, the correct formula would be 7² = 8² + 11² – 2(8)(11)cos(N). This option is not available in the provided choices, suggesting a typo in the original question. However, to address the closest correct application, we look for the equation with the proper structure:
- The side lengths squared on one side of the equation.
- The sum of the squares of the other two sides.
- The cosine of the angle we are trying to find multiplied by the product of the other two sides and subtracted from the sum of their squares.
Therefore, the second option matches this structure: 8² = 7² + 11² - 2(7)(11)cos(M). This equation implies we are solving for angle M that is opposite side 8. It's important to note that each of the provided equations could potentially be used to solve for an angle, but the question implies that only one is attempting to find the measure of a specific angle using its correct opposing side length.