Final answer:
The angle that correctly completes the law of cosines for this triangle is 120 degrees.
Step-by-step explanation:
The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of the two sides and the cosine of the included angle. To select the angle that correctly completes the law of cosines for this triangle, we need to find the angle that corresponds to the given side lengths. The correct angle can be found by rearranging the law of cosines equation and solving for the angle:
C² = A² + B² - 2ABcos(angle)
Let's analyze the answer choices:
- A. 30 degrees: If this angle is selected, the equation would not hold true for the given triangle.
- B. 60 degrees: If this angle is selected, the equation would not hold true for the given triangle.
- C. 90 degrees: If this angle is selected, the equation would not hold true for the given triangle.
- D. 120 degrees: If this angle is selected, the equation would hold true for the given triangle, complementing the lengths of the sides.
Therefore, the correct angle that completes the law of cosines for this triangle is 120 degrees.