<p>In this paper, we establish several new numerical radius inequalities for bounded linear operators on complex Hilbert spaces by employing refined versions of the classical triangle inequality. Inspired by recent developments in convex analysis and norm inequalities, we present sharpened estimates that improve upon known numerical radius bounds, particularly those involving the Moore-Penrose inverse and operator functions. Central to our approach are novel refinements and reverses of the triangle inequality, which yield tighter upper bounds through carefully constructed convex combinations and midpoint-based inequalities. These refined inequalities are then applied to derive new bounds for the numerical radius and operator norm in terms of functional calculus and polar decomposition. Our results unify and extend several existing inequalities in the literature and offer a flexible framework applicable to a broad class of operators, with potential implications for spectral theory and functional analysis.</p>