I had what I thought was a straightforward geometry problem, but found I could not solve it mathematically.because of too many unknowns.

I then sketched it in SW Part, and SW solved it. I would like to know how, which I guess is a question for mathematicians or the SW software designers.

The following image shows the SW sketch with the three known dimensions.

As you can see, the sketch is fully defined.

How does SW do this , or is there a simple mathematical solution that I have missed?

Thanks,

Bevin

PS. I am retired but like to keep my maths brain active, and usually will attempt to find a solution before resorting to SW.

By inspection they're similar triangles, therefore the two unknown (ie, not 90deg) angles are the same. Therefore only need to solve one unknown (I've gone for the smaller of the angles).

Therefore,

150 = 50cosX + 300tanX

Or

3 = cosX + 6tanX

Which looks like it should be solvable for X but I can't for the life of me remember my trig identities right now.

I think?