Use the Law of Cosines to solve the triangle. (Round your answers to two decimal places.)a= 43, b = 38, c = 74

Sure, here are the steps to solve the triangle using the Law of Cosines:

Step 1: We can start by finding one of the angles. Let's find angle A. The formula for the Law of Cosines is:

cosA = (b² + c² - a²) / 2bc

Substitute the given values:

cosA = (38² + 74² - 43²) / (2 * 38 * 74)

Step 2: Calculate the numerator and the denominator separately:

cosA = (1444 + 5476 - 1849) / (2 * 38 * 74)
cosA = (5071) / (5616)

Step 3: Divide the numerator by the denominator to get the cosine of A:

cosA = 0.903

Step 4: To find the measure of angle A, use the inverse cosine function (also known as arccos):

A = arccos(0.903)

Step 5: Use a calculator to find the arccos(0.903). Make sure your calculator is in degree mode:

A = 25.84 degrees (rounded to two decimal places)

Step 6: Repeat the process to find angles B and C. Use the Law of Cosines formula, substituting the appropriate sides. Remember that the sum of the angles in a triangle is 180 degrees, so you can use that to check your work.

Remember to round your final answers to two decimal places.