We study the problem of minimizing the number of guards positioned at a fixed height h such that each triangle on a given 2.5-dimensional triangulated terrain T is completely visible from at least one guard. We prove this problem to be NP-hard, and we show that it cannot be approximated by a polynomial time algorithm within a ratio of (1 − ε) ₁ ³⁵ ln n for any ε > 0, unless NP TIME(n ^{O(log log n)}), where n is the number of triangles in the terrain. Since there exists an approximation algorithm that achieves an approximation ratio of ln n+1, our result is close to the optimum hardness result achievable for this problem.