How to calculate a diameter of the beam on a given didtance?

[IgorFi]

Hi Gyus! Have been long away from math, but now need to solve the problem. I think it will be easy for you.

Let's say we have a beam which is 3.5 Degrees. How wide the beam diameter in meters will be, say, in 100 meters? Do you know the formula? Thank you.

 

[Dr.Peterson]

Let's say we have a beam which is 3.5 Degrees. How wide the beam diameter in meters will be, say, in 100 meters? Do you know the formula?

I think you're talking about something like a "beam" of light, which forms a cone with an angular diameter of 3.5 degrees, right?

A side view would look like an isosceles triangle with an apex angle of 3.5 degrees, and an altitude of 100 meters. Half of it will be a right triangle with acute angle 1.75 degrees, adjacent side 100 meters, and opposite side unknown. Then we have

tan(1.75°) = x/100

x = 100 tan(1.75°) = 3.055 meters

That is half the diameter you want.

 

[IgorFi]

Dr.Peterson, thank you very much. I have found an online calculator (which gave the same numbers), but not the formula. From your post I now can see how it is calculated.