Final answer:
Without additional information about angles B and C in triangle ABC, we cannot definitively determine which side is the longest. However, we know that side BC cannot be the longest since angle A is acute, and the longest side of a triangle is always opposite the largest angle.
Step-by-step explanation:
In triangle ABC, if the exterior angle at A is acute, we can infer that angle A itself must also be acute. By the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, if the exterior angle at A is acute, then angle A is smaller than the angles at B and C since any exterior angle is always larger than the interior angle it is associated with.
Given this information and the fact that in any triangle, the side opposite the largest angle is the longest side, we can determine that side BC, which is opposite angle A, cannot be the longest. Consequently, we must look at angles B and C to determine which is larger and therefore which side is the longest. Since angle A is smaller than both B and C, the longest side must be opposite the larger of those two angles. Without additional information about the specific measures of angles B and C, we cannot definitively say which side is the longest. However, we do know that side BC will not be the longest side of triangle ABC.