The method I try to use (and advocate to others so as to avoid mathematical errors) is to avoid using mathematics and plotting systems when they are not needed, that is 90% of the time. Mathematics can be avoided in most situations, apart from when you only have access from one side of the weld, such as when testing tee’s, nozzles and nodes.

To determine how far the reflector is in front of the probe without trigonometry. Follow these simple steps.

1) Maximize the reflector that you want to position. 
2) Mark a line at the front of the probe on the specimen under test
3) Record at what depth the signal maximized (Figure 66)



4) Turn the probe around 180° pull the backward until the signal appears at the same depth regardless of amplitude (Figure 67)



5) Mark in front of the probe again.
6) Bisect the 2 marks with a dot and the reflector will be directly under the dot.



As you can see in Figure 68, this method works regardless of angle, thickness and surface radius.