Calculating Length Along X-Axis for a Rotating Line

[karen_lorr]

Hi

(I hope this is the right place to post this - sorry if it's not)

Say I have a line (in the graphic is shown a 10mm but it could be any length) and it rotates around a point at one end.

What is the formula to get the length along the x-axis directly under the other end of the line. In the graphic that would be the distance between points a and x.

Thanks

K

The image is not showing so here is the link the my Hotmail onedrive file
https://1drv.ms/i/s!AlXOOGaTv36QeRu1RrJucYZFTB0

https://1drv.ms/i/s!AlXOOGaTv36QeRu1RrJucYZFTB0

EDIT - I have tried using a Taylor Series but it's been a long time since I was a school :-)
It's simple on a calculator with the cosine of the angle and the line as a hypotenous but I am trying to get the maths formula.

 

[fresh_42]

It is $x = 10 \, mm \cdot \cos (\angle{a})$.
In a right triangle $\cos (a) = \frac{adjacent}{hypotenuse} \; , \; sin (a) = \frac{opposite}{hypotenuse}$ and $tan (a) = \frac{opposite}{adjacent}.$

 

[rahul_26]

for angle $a$ made by line with x axis,length along x-axis will be $10\ cos(a)$