The angle between two lines
Richard J. Lisle, Peter R. Leyshon · Cambridge University Press eBooks · 2004
The angle between two lines in a plane (e.g. on a flat piece of paper, Fig. 16a) can be found using a protractor. Two possible angles can be quoted (α or α′ in Fig. 16a); they add up to 180°. In three dimensions the angle between two lines is defined in a similar way. It is the angle that would be measured with a protractor held parallel to the plane that contains the two lines in question (Fig. 16b). In other words, the angle between two lines is measured in the plane containing them. Figure 16b shows an example of two lines x and y . Line x plunges at 18° towards 061°, y plunges 50° towards direction 124°. The angle between them can be found stereographically in the following stages: 1 Plot the two lines, x and y (Fig. 16c). The method used is covered on pp. 22–5. 2 Find the great circle which passes through these plotted lines (Fig. 16d). This is accomplished by turning the net relative to the overlay until the points representing the plotted lines come to lie on the same great circle. This great circle represents the plane containing the two lines (the protractor in Fig. 16b). 3 Along this great circle (Fig. 16e) measure the angle (α or α′, whichever is required) between the plotted lines. In the present example, the angles are 60° and 120° respectively.