This article shows that the textbook 90 degrees-angle requirement for intramuscular injections is unrealistic. Trigonometry demonstrates that an injection given at 72 degrees reaches 95% of the depth of an injection given at 90 degrees. This relation between needle angle and needle depth, previous research into the kinematics of hand motion during an intramuscular injection, and other practical considerations support the proposal for a new, relaxed standard: Intramuscular injections administered at a comfortable angle between 72 degrees and 90 degrees.