Finding the perpendicular point in an obtuse angle

[mathhl]

Hi,

Please find the attached diagram. My goal is to find the co-ordinate point (x,y). Given that I already know the co-ordinates of A,B, and C and the length's a, b and c, how can I compute (x,y) ?.

My work: I divided them into two separate right-angled triangles and found the third co-ordinate using the slope property. I used this thread http://www.freemathhelp.com/forum/t...-set-of-coordinates-to-a-right-triangle/page2 . However, I am not sure if that's the way to proceed and how can I be sure that's the right answer?

P.S: This is not any homework problem

Thanks for your help!

 

[Bob Brown MSEE]

C is obtuse

When C is right

then denis' solution p = ab/c holds
and p²=mn because it is one of the of the Pythagorean Means.

However, you want case C>90 degrees?
Then vector analysis might be fruitful.
\(\displaystyle m=\overset{\rightharpoonup }{\text{AC}}


\cdot


\overset{\rightharpoonup }{\text{AB}}\)