Solve the following triangle using either the Law of Sines or the Law of Cosines.
\[
a=8, b=12, c=13
\]

Step 1 ：We are given a triangle with sides a = 8, b = 12, and c = 13. We are asked to find the angles of the triangle.

Step 2 ：We can use the Law of Cosines to find one of the angles. The Law of Cosines is given by: \(c^2 = a^2 + b^2 - 2ab \cos(C)\). We can rearrange this to solve for \(\cos(C)\): \(\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}\).

Step 3 ：Substituting the given values, we find that \(\cos(C) = 0.203125\). We then use the arccos function to find the angle in degrees, which gives us \(C = 78.28023969421123\).

Step 4 ：Now, we can use the Law of Sines to find the other two angles (A and B). The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. We can express this as: \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\).

Step 5 ：We can rearrange this to solve for \(\sin(A)\) and \(\sin(B)\): \(\sin(A) = \frac{a \sin(C)}{c}\) and \(\sin(B) = \frac{b \sin(C)}{c}\).

Step 6 ：Substituting the given values, we find that \(\sin(A) = 0.6025555782266653\) and \(\sin(B) = 0.903833367339998\). We then use the arcsin function to find the angles in degrees, which gives us \(A = 37.053147550366475\) and \(B = 64.66661275542229\).

Step 7 ：Final Answer: The angles of the triangle are \(\boxed{A = 37.05^\circ}\), \(\boxed{B = 64.67^\circ}\), and \(\boxed{C = 78.28^\circ}\).