I spend a lot of my time using maths to study the Sun. This is because the Sun has an impact both on our weather and also on our communications. A lot of the maths I use to do this is geometry and trigonometry. If you launch a big rocket then you need to use the maths of calculus, differential equations, mechanics and control theory. Watch the film Hidden Figures to find out more.
While my main work is in Pure Maths (Group theory), my best friend is an aerospace engineer and we often talk about his work. The short answer is that you need… all kinds of maths! You need mathematical physics and differential equations to study materials, solve fuel problems, determine the behaviour of the rocket under extreme conditions. You need calculus to compute trajectories and the exact values of acceleration that your rocket needs to get where you want it to go. You need, well, basic algebra for accounting purposes (rockets are expensive!!).
Essentially, you needs maths (and maths’ sons and daughters, applied sciences!) to control every single step of the process, and rest assured that every single step is controlled via mathematical methods.