The integration of the 60 GHz band into the IEEE 802.11 standard has revolutionized indoor wireless services. However, this band presents unique challenges to indoor wireless communication infrastructure, originally designed to handle data traffic in residential and office environments. Estimating 60 GHz signal propagation in indoor settings is particularly complicated due to dynamic contextual factors, making it essential to ensure adequate coverage for all connected devices. Consequently, empirical channel modeling plays a pivotal role in understanding real-world behavior, which is characterized by a complex interplay of stationary and mobile elements. Given the highly directional nature of 60 GHz propagation, this study addresses a seemingly simple but important question: what is the impact of employing highly directive antennas when deviating from the line of sight? To address this question, we conducted an empirical measurement campaign of wireless channels within an office environment. Our assessment focused on power losses and distribution within an angular range while an indoor base station served indoor users, simulating the operation of an IEEE 802.11ad high-speed WLAN at 60 GHz. Additionally, we explored scenarios with and without pedestrian movement in the vicinity of wireless terminals. Our observations reveal the presence of significant antenna lobes even in obstructed links, indicating potential opportunities to use angular combiners or beamformers to enhance link availability and the data rate. This empirical study provides valuable information and channel parameters to simulate 60 GHz millimeter wave (mm-wave) links in indoor environments, paving the way for more efficient and robust wireless communication systems.