Adding line of specific length between two existing lines to form isosceles triangle

[tortoise]

Hello,

 

I have 2 lines intersecting at an acute angle (say 60 degrees, for example). I want to add a third line with a specific length (say 2.6 metres) perpendicular to the center-line of the other 2 lines to form an isosceles triangle. Is my explanation clear? What's the best and easiest way to add this third line? Is it possible to do without working out the trigonometry?

 

Thanks,

[Dadgad]

Welcome to CADTutor tortoise!

 

If the angle is a known 60 degrees, create a circle with the same radius as the length of the side you want to add, at the point of intersection of the first two lines.

That line should intersect each of the other legs at points which will define the end points of your new side. No muss, no fuss, nor tedious calculations.

But that is a one off solution, if the angle is 60 degrees only.

 

For any other angle, just create an angle bisector between the two lines, and offset that line by one half of the length of the new side, in both directions, it will define your endpoints for the new line.

 

No doubt there is a more elegant way to approach this, which I look forward to seeing, but that gets the job done, albeit somewhat tediously.

Edited August 6, 2016 by Dadgad

[tortoise]

Thanks Dadgad,

 

Sorry: 60 degrees was a very badly chosen example angle! I would like to know if there is a solution for any angle - say 37 degrees.

[tortoise]

Oh! I understand your solution now. So simple! Thanks!

[Dadgad]

Thanks Dadgad,

 

Sorry: 60 degrees was a very badly chosen example angle! I would like to know if there is a solution for any angle - say 37 degrees.

 

Well from my perspective at that point in time, it was a perfect example, as it was the easiest possible case scenario!

And I hadn't yet come up with the other way, so no harm, no foul!

 

That's what I like about geometry, it is all so intuitive, ever since the Greeks figured it all out.

I hate trigonometry, it just bores me!

 

Glad I could help you.

Edited August 6, 2016 by Dadgad