Drawing Triangles Given Lengths of 3 Sides

In doing renovations to my back yard, I needed to figure out some angles. The back yard is hilly, and the contractor needed to know the angle of the slope. He had measured three lengths of a triangle, and asked me to determine the interior angles.

The lengths were 102", 102", and 90". I fired up AutoCAD, and quickly worked out the angles. How would you approach the problem? The difficulty is knowing where the three lines intersect.

I relied on a technique learned in my days of hand drafting. The solution back then was as follows:
1. Draw one of the three lines. The ends of the line locate the first and second corners of the triangle.
2. Set the compass to the second distance, and draw an arc.
3. Change the compass to the third distance, and draw another arc.

The intersection of the two arcs is the third corner of the triangle. The same technqiue works in CAD, except that we would use circles instead of arcs. With the triangle drawn, the three angles can be measured.

P.S.

Writing up this tip made me think about how it is easier to draw arcs in hand drafting, and harder to draw arcs with CAD. The opposite is true for circles: harder in hand drafting, easier in CAD. Makes me wonder why.

Comments

[Evan Yares]

It would have been easier to draw using a line and two circles.

Phil Kreiker once mentioned to me that he didn't even teach the AutoCAD Arc commands in his classes at the Colorado School of Mines. It's faster to draw circles and trim them.

In any case, the reason it's easier to draw circles than arcs is that there are a lot of different ways to draw arcs.

AutoCAD at least, circles are represented by a center and radius, with arcs having an additional starting and ending angle.

I actually had to check this... and was a little mystifed by it. I expected AutoCAD to store at least a full coordinate for the first point, and possibly an included angle -- but no.

The problem here is that, for shallow arcs (with numerically high radii) the calculation of the starting and ending angles is subject to transcendental math errors. This is not a good thing. If I were a surveyor, I'd be more than a little nervous about this.

Interestingly, polyarcs do store starting and ending points, so they are a much better choice when you need to draw with high precision. Unfortunately, they're not even as easy to use as regular arcs.

To me, this is an excellent example of why "bog-standard" CAD systems are so limited, and why parametric CAD systems have so much more power.

In a parametric CAD system, you just draw a rough triangle, then apply a dimension constraint to each side and set the appropriate length, and apply an angle measurement to each corner. (You may need to tell the system the corner angle measurements are "reference dimensions", because you will be over-constraining the triangle if you try to set three side lengths AND 3 corner angles).

Now you can edit any or all of the applied dimensions and immediately get a regenerated triangle with all dimensions and angles instantly and accurately updated - no erasing and re-drawing required. The same principles will work with any level of complexity of figure which you are drawing, and the benefits of parametric modelling grow as the complexity increases.

So tell me - why DO people persist with non-parametric CAD systems, when there are alternatives which are so much more powerful?

[R.K. McSwain]

Sounds like a 'distance-distance intersection' COGO problem, which always produces zero or two possibilities.

[lev]

Google is your friend.

http://ostermiller.org/calc/triangle.html