Unmanned Aerial Systems (UAS) have the potential to provide cost effective solutions to many problems, but their control systems need to be safe and trustworthy in order to realize this potential. In this paper we show how behavior trees (BTs), created using backward chaining and using a particular way of labelling subtrees, can be used to meet the requirements of trustworthy autonomy described in a US air force (USAF) report. Behavior Trees represent a modular, reactive and transparent way of structuring a control system that is receiving increasing interest in the UAS community. While their safety and efficiency have been investigated in prior research, their connection to trustworthy autonomy has not been explored. A set of guidelines for trustworthy autonomy, taken from a USAF report, include items such as: being similar to how humans parse problems, being able to explain its reasoning in a concise way, and being able to be visualized at different levels of resolution. We propose a new way of deriving explanations that conform to these guidelines, using a particular labeling of subtrees in the BT combined with a structured design methodology called backward chaining. The proposed approach is illustrated in a detailed example.