Final answer:
The 'steeple sign' on an AP soft tissue neck x-ray, appearing as a long triangle shadow, indicates croup, leading to the correct answer being 'b. Steeple, croup'.
Step-by-step explanation:
The characteristic sign on an AP soft tissue neck x-ray that appears as a long triangle shadow in the trachea is indicative of croup. This radiographic finding is known as the steeple sign. In contrast, the sign associated with epiglottitis is often referred to as the thumbprint sign due to the swollen appearance of the epiglottis. Tonsillitis does not typically show a distinctive sign on a neck x-ray, and there is no peak sign associated with croup. Therefore, the correct answer is b. Steeple, croup.