Question regarding angles and distances on a plane

[CigmaChi]

Hey guys,
I had a question, not really a homework assignment but more of a just wondering question. Please look at my photo of the drawing that I drew to scale on graph paper. So my question is if you have a laser that is lets say 50 units from the plane, and you move it exactly 10 degrees (i chose 10 just for the **** of it) is there any way to calculate the distance the laser moves on the plane. I know that the distance between the laser and the plane increases,which increases the distance on the plane, however I was wondering if there is any formula or percentage that you can calculate the distance of space being used with a set increment of degrees. I tried measuring the distance out in mm as close as I could and could not recognize any pattern or set fractions.

Please look at my drawing, thanks again everyone and happy Friday

 

[Ishuda]

Hey guys,
I had a question, not really a homework assignment but more of a just wondering question. Please look at my photo of the drawing that I drew to scale on graph paper. So my question is if you have a laser that is lets say 50 units from the plane, and you move it exactly 10 degrees (i chose 10 just for the **** of it) is there any way to calculate the distance the laser moves on the plane. I know that the distance between the laser and the plane increases,which increases the distance on the plane, however I was wondering if there is any formula or percentage that you can calculate the distance of space being used with a set increment of degrees. I tried measuring the distance out in mm as close as I could and could not recognize any pattern or set fractions.

Please look at my drawing, thanks again everyone and happy Friday

Call the straight up and down line, the one 90 degrees to the (cross section of the ) plane, the 'adjacent' line and the line along the plane the 'opposite' line. Now look at an individual triangle formed by the adjacent line, the opposite line and the hypotenuse [the line at the 10 degree angle (or any angle)]. This is a right angle triangle. Thus given the angle between the base and hypotenuse and the length of the base, the trig functions will give you the length of the other lines:
cosine(angle) = adjacent/hypotenuse
sine(angle)= opposite/hypotenuse
etc.

Now that you have the distances for the individual sides of all the right triangles, simple subtraction will give you the length the laser moves from one triangle to another.

 

[CigmaChi]

Question about distance each angle makes on the plane

So my question is now does the distance that each adjacent 10 degree angle makes on the plane have any ratio or follow some sort of mathematical pattern that would allow me to calculate the distance the laser makes on the plane for the next 10 degree angle. Is there any relationship to calculate the increase in distance on the plane for each adjacent angle that gets larger and larger? Like is there a increase percentage or any mathematical laws? For example in my drawing each 10 degree angle makes a distance 10, 13, 18, 26, 48 mm. Is there any way to know what the distance the next 10 degree angle would make? Is there a formula or ratio or some mathematical relationshop to the distance increase to each adjacent angle of the same degree?

 

[stapel]

So my question is now does the distance that each adjacent 10 degree angle makes on the plane have any ratio or follow some sort of mathematical pattern....

The previous reply explained exactly how to find the "mathematical pattern", specifying how to use trig ratios to do so. Try doing what is suggested there.