Is there a solution for this isoceles triangle problem?

[davedave]

Again, this is NOT a homework problem.

Here I am posting a second problem from the math book, The Solvable and the Unsolvable,
which I found in the library.

Consider the isoceles triangle ABC and point D is a point on the side AB.

Please see the diagram below and IGNORE the dots which are used to show the positions of the vertices of the isoceles triangle.

......A



...D

...B______________C

suppose that side AB=side AC. angle BAC=20 degrees and angle BDC=30 degrees.

Prove that side AD=side BC.

Is it possible to prove? If it is, how do you do it?

any ideas? There are lots of interesting problems in this book.

 

[oen_maclaude]

hi! i tried this problem by construction. But I don't know if it is good to prove by this method.

 

[Georgepowell]

AD = [AC*sin(10)/sin(150)]
BC = [AC*sub(20)/sin(80)]

and just using a calculator you can show that

sin(10)/sin(150) = sub(20)/sin(80)

So AD = BC.