The correct answer is: A. measuring approximate horizontal angles.
A cross staff is a simple instrument used for measuring approximate horizontal angles. It consists of two flat pieces of wood or metal, each with a sighting hole at one end. The pieces are held together at right angles by a pivot, and the instrument is used by sighting through the two holes at a distant object. The angle between the two sighting lines can then be read off a scale on one of the pieces of wood.
Cross staffs were used by surveyors and navigators for centuries, before being replaced by more accurate instruments such as the theodolite. They are still used today by some traditional craftspeople, such as carpenters and boat builders.
Option B is incorrect because a cross staff cannot be used to set out right angles. To set out a right angle, two lines must be drawn at right angles to each other. A cross staff can only measure the angle between two lines, not the angle between a line and a point.
Option C is incorrect because a cross staff cannot be used to measure bearings of lines. A bearing is the angle between a line and a north-south line. A cross staff can only measure the angle between two lines, not the angle between a line and a north-south line.
Option D is incorrect because a cross staff is an instrument used for measuring approximate horizontal angles.