The number of collaborations between humans and artificial agents has risen steeply in recent years due to the rapid expansion of AI. Numerous studies in social sciences have already established that trust is a crucial factor in ensuring effective teamwork. While the dynamics of trust in human-human relationships or the effects of human comportment on the artificial agents' trustworthiness have been researched, the changes in human trustworthiness as a result of different AI behaviors were scarcely analysed. Therefore, the latter perspective needs to be thoroughly studied as well. This paper has investigated how an AI directing the human can affect human trustworthiness. So far, the directability has been studied as a notion on its own without being linked to trust or its effects on human-AI relationships. For this research, subjective and objective measurements have been used to assess the effects of an AI directing the human in joint activity. In order to quantify the human trustworthiness and assess the possible changes, an experiment has been carried out where participants played a Search & Rescue game developed in the MATRX software. The human's trustworthiness has been calculated using the ABI model and a questionnaire. The obtained results suggest that there is not a significant change in human trustworthiness as a result of the artificial agent directing the human.