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I think this is best described by the picture below

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Given coordinates for point A and B, and their angles (a and b), which formula can I use to get the coordinates for point C ?

Rafael Werlang
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  • Instead of thinking of using a formula, think of using your head to find a formula. I.e. the formula is the last step, not the first. – Michael Hardy Dec 26 '14 at 20:16
  • @MichaelHardy I tried to find a formula, I asked my dad and my brother for help, both engineers, they said it was not possible. Maybe they misunderstood the question. I am not well versed into trigonometry, so I spent almost an entire night trying to figure out proportions and coming up with some equations. I gave up cause I know it would be smarter to ask for help from qualified persons, like yourself, sir. Thank you and Henning Makholm for the awesome quick reply. – Rafael Werlang Dec 26 '14 at 20:52
  • If you told your father and your brother what you told us, then it would be irrational for them to say simply that it's not possible. – Michael Hardy Dec 26 '14 at 21:13

2 Answers2

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The two blue lines have the equations $$ k = -\tan(a)\cdot j $$ $$ k = -\tan(b)\cdot (x-j) $$ Solve this system of equations for $j$ and $k$.

hmakholm left over Monica
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$$ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac k j = -\frac{\text{opposite}}{\text{adjacent}} = -\tan a. $$ So the equation of the one of the lines is $y = -(\tan a)x$.

Similarly, the other one is $y=(\tan b) (x-x_0)$, where I take the coordinates of the point $B$ to be $(x_0,0)$.

So you need $$ (\tan b) (x-x_0)=-(\tan a)x. $$ $$ (\tan b+\tan a)x = (\tan b)x_0 $$ $$ x= \frac{(\tan b)x_0}{\tan b + \tan a}. $$ $$ y = \frac{-(\tan a)(\tan b)x_0}{\tan b + \tan a}. $$

Michael Hardy
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  • Maybe you can help me with this question: http://math.stackexchange.com/questions/1556534/triangle-formula-for-alternative-points Thanks! – John Smith Dec 02 '15 at 20:52