# Bearing to X,Y, Z

I’m working on a small project where I’m testing the ability of a laser to accurately measure the angle of a wire. My control for the experiment gives me X,Y,Z coordinates for a point on the wire and the laser gives a distance and a bearing to the point on the wire. Is there a simple calculation that I can do in excel that will transfer from distance (m) and bearing (deg).

• This is a math problem (computational geometry) with no clear GIS component. – Vince Jan 14 '16 at 12:03
• Thanks for the advice; have posted in another forum now also. – Rich Jan 14 '16 at 12:49
• This is a measurement (geomatics) problem. I thought geomatics was On Topic! – Martin F Jan 15 '16 at 4:08
• This question has been put on hold at math.stackexchange.com/questions/1612145/bearing-to-x-y-z, and had a migration from there to Mathematica rejected. Although it is not a "question about GIS", if it does not re-open at Mathematics then I think we should be sympathetic to it re-opening here because it is not far outside the scope of GIS and appears to be from a surveyor. – PolyGeo Jan 15 '16 at 6:09

Form (whole circle) bearing, zenith angle and horizontal distance to X, Y, Z

X = X0 + h_distance * sin(deg / 360 * pi()) Y = Y0 + h_distance * cos(deg / 360 * pi()) Z = Z0 + h_distance / tan(zenith / 360 * pi()) 

• X0, Y0, Z0 are the coordinates of the station
• deg / 360 * pi() changes angle from deg to radians

Horizontal distance from slope distance and zenith angle (deg)

h_distance = s_distance * sin(zenith / 360 * pi())

• Thanks for the reply. In my set up I'm not recording a zenith angle, is there a way to do the calculation without? Rich – Rich Jan 14 '16 at 10:57
• Only if you use the Z coordinate from the control, rearrange formula for Z to express zenith angle. This way you cannot control Z only X and Y. Other possibility if all the distances are in the same plane, you can use that plane as XY plane (e.g.zenith angle is 90 degree). – Zoltan Jan 14 '16 at 17:13