1. Street Sideline Intersection

Two intersecting streets are shown on the right. The centerline direction for each is known as are their widths.

Given the coordinates of a point on each centerline, what are the coordinates of the sideline intersection at point P?

 

sl1

 

sl2

Since bearings are given, this is a bearing-bearing intersection.

Because point P is not on the centerlines it should not be connected directly to the two given coordinate points.

Instead, create two new points, G and H, on each sideline. These will serve as the baseline for the intersection triangle.

 

sl3

sl4

To create point G, go perpendicular to the centerline at the given coordinate:

eqn01

 

eqn02

 

sl5

sl6

Do the same to create point H:

eqn03

 

eqn04

 

sl7

Inverse to determine the length and direction of the baseline GH:

eqn05

 

sl8

Sidelines have the same directions as their respective centerlines. Using those, compute the three angles:

eqn06

 

 

sl9

Then using the Law of Sines, determine the two missing sides:

eqn07

 

sl10

Compute point P from point G:

eqn08

 

Math check - compute point P from point H:

eqn09
check