How to Find the Distance of Parallel Lines Cut by a Transversal
- 1). Label the two points of intersection A and B.
- 2). Draw a line segment from the point of intersection of the transversal and one of the parallel lines, to the other parallel line, so that the point of intersection for the line segment and the second parallel line forms a right angle. Label the right angle C.
- 3). Use the protractor to measure the angle BAC, unless the size of the angle is already known. Measure the angle ABC as well.
- 4). Find the sine of the angle that is on the same parallel line as the right angle. That is, if points A and C are on the same line, find the sine for angle BAC, but if points B and C are on the same line, find the sine for angle ABC.
- 5). Set up the equation sin (BAC)=d/l, where "d" is the distance between the two parallel lines and "l" is the length along the transversal between points A and B. (If points B and C are on the same line, find the sine for ABC instead.) For example, suppose the measure of angle BAC was 30 degrees, and the length between A and B was 5 inches. The sine of 30 degrees is 0.5, so the equation would read 0.5 = d / 5.
- 6). Multiply both sides of the equation by the length between A and B (in this case 5 inches) to find the distance between the two parallel lines. So 5 * 0.5 = 5*d / 5. This simplifies to 2.5 = d, so in this example the distance between the two parallel lines is 2.5 inches.
