Final answer:
The angles of the triangle are approximately 131 degrees, 47 degrees, and 2 degrees.
Step-by-step explanation:
To find the angles of a triangle, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c and angles A, B, and C, the following formula holds: c^2 = a^2 + b^2 - 2ab * cos(C). Plugging in the given values, we have: 4^2 = 2^2 + 3^2 - 2*2*3*cos(C). Solving for cos(C), we get: cos(C) = (-7/12). Taking the inverse cosine of -7/12, we find that angle C is approximately 131 degrees.
Next, to find angle A, we can use the Law of Sines. The Law of Sines states that in a triangle with sides a, b, and c and angles A, B, and C, the following formula holds: sin(A)/a = sin(B)/b = sin(C)/c. Plugging in the values, we have: sin(A)/2 = sin(131)/4. Solving for sin(A), we get: sin(A) = (2/4) * sin(131) = (1/2) * sin(131). Taking the inverse sine of (1/2) * sin(131), we find that angle A is approximately 47 degrees.
Finally, we can find angle B by subtracting angles A and C from 180 degrees: 180 - 131 - 47 = 2 degrees. Therefore, the angles of the triangle are approximately 131 degrees, 47 degrees, and 2 degrees.