SOLUTION: Dear Edwin McCravy, Hopefully you are very fine. Your previous solution worked very well. Now I am asking for another solution. If I have the length of the base of a tria

Algebra ->  Triangles -> SOLUTION: Dear Edwin McCravy, Hopefully you are very fine. Your previous solution worked very well. Now I am asking for another solution. If I have the length of the base of a tria      Log On


   

Question 716018: Dear Edwin McCravy,

Hopefully you are very fine. Your previous solution worked very well. Now I am asking for another solution.

If I have the length of the base of a triagle, an obtuse angle adjacent to the base and the difference between the other two sides of the traingle, how can I draw the triangle.

Thanks for your kind perusal and I would be grateful if you please provide me with the solution.

Best regards.
Sharif Taufique Atique
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
We are given AB, obtuse ∠BAC (but we do not have point C.  I placed
C? at an arbitrary place along that side of the given
angle, and we are given the length of BC-AC, the green line segment below.
We want to draw ߡABC.



We extend CA so that AD = BC-AC 

 

We draw DB

   

We want to find the point on CD such that BD is the base
of an isosceles triangle.  We do this by constructing the
perpendicular bisector of BD, which will be the base of the
isosceles triangle.  We know that the perpendicular bisector of
the base of an isosceles triangle passes through its vertex.
That perpendicular bisector is the blue line:



The point where the blue line intersects CD is the desired
point C.  We draw the line from that point to B:



ߡCDB is isosceles, so BC = DC, CD - (BC-AC) = BC - (BC-AC) = AC.

So we have drawn ߡABC.

Edwin