The correct answer is A) A tangent bearing of the headland to the south-southeast should be corrected by adding one-half of the beam width. This is because when a vessel is close to a headland or other prominent feature, the radar image of that feature can distort the apparent bearing of the object. To correct for this effect, the tangent bearing should be adjusted by adding half the beam width of the radar beam. This helps account for the widening of the radar beam as it reflects off the headland. The other options are incorrect because: B) Ship No. 1 is likely detected, just obscured by the shadow effect of the headland; C) The small island may not be detected due to its small size, not the beam width; and D) Ship No. 2 is likely detected, but its reflection may be overpowered by the larger mountain in the background.