Bluetooth Low Energy (BLE)-based trilateration is attractive for indoor positioning because it can operate with low-cost infrastructure, yet RSSI-derived distances can become geometrically incompatible in real deployments. This study characterises those failure geometries using 162 million raw RSSI records collected from Emergency Room and Office deployments at Diponegoro National Hospital, Indonesia, from which 12.9 million synchronised three-scanner observations were analysed. Four recurring Trilateration Failure Modes (TFMs) are quantified across two deployments, three LDPL exponent scenarios, and raw versus Kalman-filtered RSSI. Failure-mode prevalence depends jointly on deployment and the assumed RSSI-to-distance model: TFM-I dominates several conditions, whereas TFM-III becomes dominant under higher-attenuation assumptions, with the transition occurring at different scenarios in the two deployments. To contextualise the Radius Adjustment Intersection Method (RAIM), two deterministic geometric baselines are evaluated: a common-factor Uniform Radius Scaling (URS) baseline and a Paek-style pairwise incremental adjustment. A common scale factor is feasible for 23.63–96.34% of observations, showing that a single multiplicative correction cannot reconcile all observed circle configurations. The Paek-style adjustment and RAIM both recover near-complete three-circle feasibility, but they produce different correction magnitudes and coordinate displacements. RAIM retains the smallest RSSI-derived radius as an anchor and sequentially adjusts the remaining radii. These outcomes are interpreted as geometric constraint-satisfaction and spatial-plausibility results rather than absolute localisation accuracy because ground-truth coordinates were unavailable. Anchor-sensitivity analysis further shows that alternative anchor choices can shift estimated coordinates by several metres, while room-polygon outlier status changes by less than 0.06%. The results identify deployment-dependent failure geometry, correction-model choice, and anchor selection as considerations for low-cost BLE trilateration.