Final answer:
NASA needed Katherine Johnson to perform Trigonometry to make accurate calculations for space missions.
Step-by-step explanation:
For the mathematics that NASA needed Katherine Johnson to perform, the answer is Trigonometry. Trigonometry involves the study of angles and their relationships in triangles, which is crucial for calculating orbital mechanics and trajectories in space missions. Through the application of trigonometry, Katherine Johnson was able to make accurate calculations that contributed to the success of NASA's spaceflights, including the first moon landing.