How to calculate sensor spot size from viewing angle?

Question

Geometry

Greetings.
Tell me how to calculate the "spot" of the sensor knowing the viewing angle?
Let's say there is an object, two meters per meter. I would like to know at what maximum distance I can remove the sensor so that the object is completely placed in the field of view of the sensor. But at the same time, so that the sensor does not capture the space on the sides.
The viewing angle of the sensor is 5 degrees.
It looks something like this:

If you need more data, I'll try to get it.

Answer 1

This is clearly an isosceles triangle.
1. find the side (beam at the edge of the viewing angle)
a = b/(2sin(β/2))
where b = 1m
β = 5°
a = 11.46
2. find the distance of the segment that passes from the vertex of the triangle from 5° to the center of the segment 1m
d = sqrt(a^2 -( b/2)^2)
d = 11.44

Answer 2

Have you not taken trigonometry yet, or is everything so bad with education?
0.5m/tg(5deg/2)=11.45
0.5m*ctg(5g/2)=11.45

Answer 3

Can b = max(1,2)