Triangle ABC is isosceles with AB=AC. Point D is on side AB such that angle BCD is 70 degrees. Point E is on side AC such that angle EBC is 60 degrees. Angle ABE equals 20 degrees, and angle DCE equals 10 degrees.

Find angle EDC. Justify your answer.

Consider a convex quadrilateral with angles named as in figure (T,W,X,Y.Z). Of course the pic is a rectangle; generalize :-)

----------
|\     W/|
|X\    / |
|  \T /  |
|   \/   |
|   /\   |
|  /  \  |
| /    \Z|
|/Y     \|
----------

Then the following is a formula one gets from multiple applications of the law of sines:

1=(sin(W)/sin(T+W))*(sin(X)/sin(T-X))*(sin(Y)/(T+Y))*(sin(Z)/sin(T-Z))

Isn't this awesome?!? Of course, it gives what Charlie and others got, and I don't think it reduces without introducing vectors or something :-)

Now to figure out how to do this one constructively ...

Posted by owl on 2004-11-04 02:58:07