Final answer:
The Law of Cosines is used to find the length of side xZ in a triangle given the lengths of the other two sides and the included angle. The formula c² = a² + b² - 2ab cos(γ) is applied in a step-by-step process, which includes subtracting the product of the sides and cosine of the angle from the sum of the squares of the sides and then taking the square root.
Step-by-step explanation:
The Law of Cosines is used to calculate the length of a side in a triangle when two sides and the included angle are known. The formula is c² = a² + b² - 2ab cos(γ), where a and b are the lengths of the sides of the triangle, and γ is the included angle. To find side xZ, identify the lengths of the other two sides and the angle opposite to xZ, then substitute these values into the Law of Cosines formula to solve for xZ.
Step-by-step:
- Identify the lengths of sides a and b, and the measure of angle γ.
- Plug these values into the Law of Cosines formula: c² = a² + b² - 2ab cos(γ).
- Calculate a² and b².
- Calculate 2ab cos(γ).
- Subtract the result of step 4 from the sum of the squares of sides a and b.
- Take the square root of the result to find the length of side xZ.