What is a specific example of geometry in electrical engineering?

Question

I need a math problem that shows how geometry is used in the job, explaining the specific situation using numbers. I know geometry is used in process control equations to control the valves, but what is a specific example of this? (It can be trigonometry, similarity, geometric means, segments and angles in circles, special right triangles, vectors, Law of Sines/Cosines, Pythagorean theorem, area, perimeter, volume, transformations, etc.) Thank you!

Answer 1

Basic Power Triangle: Apparent, Real and Reactive power
S = apparent power
P = real power
Q = reactive power

real power (heat) is along the x-axis.
reactive is the y-axis.
apparent power is the hypotenuse.
S = P + jQ
so
S = VI cos theta + jVI sin theta
and
S= (P^2 + Q^2)^1/2
so
cos theta = (P/S)
sin theta = (Q/S)
tan theta = (Q/P)
Theta is the angle at which the current either lags or leads the voltage.
So if the impedance is
Z = R +jX (or Z I is the current
V is the applied voltage, make 120V at 0 degrees
I = V/Z, this will be a complex number. Any numbers can be plugged into the power equations above.
This all ties in with the previous answer detailing an RC circuit, actually RL in this case.

Answer 2

If you have a sine wave applied to an RC series, then the 2 voltages (across the R and C) will be like a cosine and sine respectively, so they combine according to the Pythagorean theorem.