Find ∠α∠𝛼 given the following values:a=𝑎= 12 b=𝑏= 10 c=𝑐= 15

To find the angle α (alpha), we can use the Law of Cosines. The Law of Cosines states that c² = a² + b² - 2ab*cos(α).

Given that a = 12, b = 10, and c = 15, we can substitute these values into the formula:

15² = 12² + 10² - 21210*cos(α)

225 = 144 + 100 - 240cos(α)

225 = 244 - 240cos(α)

Subtract 244 from both sides:

-19 = -240cos(α)

Divide both sides by -240:

cos(α) = 19/240

Now, to find the angle α, we need to find the arccos (or inverse cosine) of 19/240.

α = arccos(19/240)

Using a calculator, we find that α ≈ 81.41 degrees.