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The target is in the shape of a U where the horizontal segment is 20 inches, and the two vertical segments are 14 inches. We are using a camera to image the target, and then using vision processing to isolate the target from the rest of the image. We know the vertical field of view, and the horizontal field of view of the camera. The resolution of the camera is 640x480 pixels.

The vertical distance between the camera on the robot and the target is constant but as of yet unknown because the robot hasn't been constructed yet. It is known, however, that the target will always have a higher elevation than the camera.

How can we use this data to calculate in real time the robot's distance to the target, and the angle to the target?

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I would suggest model based pose estimation. DeMenthon and Davies describes a method for finding the pose of an object using 25 lines of Code!

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