# For all you math geniuses out there

I have an empty that is the base of my character’s movement. It is the parent to my character object. That character object has a vertex which is a vertex-parent to a camera. At one point I want to be able to rotate my empty (and obviously the character) forward along the x-axis 30 degrees. How far do I need to move my camera in x, y, z coordinates to keep up with that action? Also, how far do I need to rotate the camera to keep the character in the same perspective?
The vertex is 70 blender units directly up along the z axis from the empty that the whole character moves around. The camera is an additional 160 units above that and also 110 units behind it along the y axis (thus it is a total of 194.164878389476 units in a direct line from the vertex). Furthermore, the camera is angled downwards around the x axis 60 degrees to see the character. Please note, I am not only looking for an answer, but what the equations are that led to that result (in case I decide to tweak distances and angles later). Thanks.
Oh, and I should add, I do not know exactly what angle/location my empty, character, or camera will be at any given moment. As such, all the dimensions I gave are LOCAL, not global, and the equations to solve this need to be able to work regardless of the current locations/rotations.

You don’t have to be a “math genius” to add a level of indirection:

The character should be vertex-parent to an empty, which should be a parent to a camera.

All you have to do then is move/animate the camera relative to the empty - How much and how far is something you can figure out through trial and error.

Haha! Nice one Goran!