Hi,

I am a bit rusty in the math department and I have been puzzeling with a problem I could use a hand with.

Imagine a triangle divided into two sub triangles.

I know A and B as well as a and b. I also know that a and b are the same length.
My approach has been to write up the law of sines for the three triangles (the two inner and the outer)

sin(A)/a = sin(C)/c = sin(D)/d

sin(B)/b = sin(E)/e = sin(F)/f

sin(A+B)/(a+b) = sin(C)/e = sin(F)/d

as well as eliminating the variables that are identical

c = f

a = b

This leaves me with

sin(A)/b = sin(C)/f = sin(D)/d

sin(B)/b = sin(E)/e = sin(F)/f

sin(A+B)/(2*b) = sin(C)/e = sin(F)/d

I have a hard time getting further, and I am unaware if the problem is underconstrained.

Ultimately I am seeking to know d, f and e. Ideally as a function like:

def calculate(A,B,b):

return (d,f,e)

How would you attack the problem?

Kind regards

Jesper

taxfromdk said:
How would you attack the problem?

It would help if you gave a complete problem description (ie what information do you have and what information do you need to know?), rather than a description of an incomplete attempt to solve an unknown problem, I think.

For what it is worth, angles in triangles have a sum of 180 degrees (I think, too many years ago), D+E is also 180 degrees assuming the top line is straight. Also, to make your own life simpler, use one name for known equal length or equal angles (just a instead of a and b, and just c instead of c and f, for example.

EDIT: Right you wrote the description near the bottom, missed that completely.

taxfromdk said:
Ultimately I am seeking to know d, f and e. Ideally as a function like:

def calculate(A,B,b):

return (d,f,e)

How would you attack the problem?

Thinking about it, I am not seeing a solution. For the right triangle depending on unknown angle E, f can get long or shorter. At the very least you'll get 2 solutions (E larger than 90 degrees,. draw a circle with center point at F, and radius b, line f will cross the circle at 2 points).

For different angles A and B and a straight line from corner C to corner F, a == b seems impossible to me.

taxfromdk said:
def calculate(A,B,b):

Seems the problem is undetermined.

If i sum up AB and ab to define the single bounding triangle, the applet i've found is not happy:

Obviously side a and side b as above could have various unknown lengths to work with my two inputs.

I guess you overlook something, and adding it to the problem definition will help.

I asked a colleague for help and he found a solution, that he posted at https://math.stackexchange.com/questions/4757385/is-it-possible-to-determine-sides-in-a-triangle-given-angle-of-median-and-opposi/4757531#4757531​

Thank you for your help, I learned something today 🙂