OK, in that case, changing a resistance is not really required. Simply use a microcontroller to keep track of the position and then use PWM or something similar to control the LED brightness.
Also note that a sensor like this doesn't calculate angle, it is sensitive to acceleration. Because of this it can be hard (or impossible) to tell the difference between the device being held at an angle (and thus you measure the direction of the gravitational field) or being moved an accelerated through space in such a way as to generate the same forces that would have resulted from it being held statically in a certain position.
There are other detectors that can determine their orientation in space independently from the acceleration they undergo. One of these sensor (often labelled as being "6 axis" or similar) if you wish to determine both orientation and acceleration -- and therefore be able to estimate position.
Here is a "9 axis" device which incorporates gyroscope (orientation), accelerometer, and magnetic field (roughly direction and dip) measurements. Note that it also appears to have a barometric sensor as well.
From your very limited explanation, the gyroscope sensor would seem be best suited to determine orientation than would an accelerometer.