I Need help coming up with an equation for a bend angle calculation

[nddwind]

Apologies if this is the wrong forum.

I have an application where I need to measure the bend angle of a tube and display the resulting angle on a screen. I am using a laser mounted in a fixed location which reports distance back to my controller, (scaled to millimeters.) I am measuring from 92 degrees to 88degrees with 90 degrees being nominal. Is there a formula for converting a distance measurement to an angle? I am aiming to achieve .05degree resolution, so 90.05degrees, 90.1, 90.15, etc.. At first I thought that because the distance and range that I was measuring was so short I could use a simple linear equation to scale my distance to an angle but it seems that the rate of change between each degree is much higher than I thought. Also if it helps I'm about 18 inches away from the bend radius.

I am pretty terrible at math, and I'm not even sure if this would be described as a differential equation that I am looking for.

I've attached a picture if it helps.

Thank you for your time.

 

[FactChecker]

More information is needed. Is 18 inches the horizontal distance from the laser to the tube at $90\deg$? What is the vertical distance from the tube pivot point to the laser intersection point?

 

[nddwind]

Vertical distance from pivot point to the point on the tube that the laser hits is roughly 311mm, horizontal distance is 100mm from tube at 90 degrees. (the 18inches I provided was way off)

Thank you

 

[FactChecker]

Try angle=atan2d((100-x), 311) + 90, where x=distance from laser to tube in mm and the angle is less than 90 when the distance is greater than 100.

 

[nddwind]

Thank you for the reply, how would I use atan2d, or how could I enter that equation into a online calculator like desmos

 

[nddwind]

Think I got it, thank you

 

[nddwind]

Is there another way to write the atan2d function? Or write the equation you gave without using the atan2d function? My controller doesn't have that math option

Thanks for all the help

My controller does has atan and atan2 instructions

 

[Office_Shredder]

I believe the only difference between atan2 and atan2d is the first is in radians and the second is in degrees