In Triangle ABC, AC = BC and mC = 62°. The longest side of the triangle is:

AC
BC
AB
AM

If C=62, then A=B=(180-62)/2 = 59

So, AB is the longest side.

To find the longest side of triangle ABC, we need more information about the triangle. The given information that AC = BC and angle C is 62 degrees does not provide enough information to determine which side is the longest.

In a triangle, the side opposite the largest angle is always the longest, while the side opposite the smallest angle is always the shortest. However, in this case, we don't have enough information about the other angles or sides to identify the longest side.

To determine the longest side, we need either the measures of two angles or the lengths of two sides. With additional information, we can apply the triangle inequality theorem or use trigonometric functions to compare the lengths and angles in the triangle and identify the longest side.

If you have any additional information about the triangle, such as the measurements of other angles or sides, please provide them, and I can assist you further in determining the longest side.