This problem is very intresting, as I first got the correct answer using analytic geo, but wondered if there was another, easier way to do this.
If ΔBCD is isosceles and ㄥADC = 105° and BC = 5√6, find AC in the figure below:
If ΔBCD is isosceles and ㄥADC = 105° and BC = 5√6, find AC.
∠ADB = 1/2 (105º) ∠ABD = 90º - ∠ADB AB = BC
AC = 2 (sin∠ABD * 5√6)
Please be careful when you are answering, ABD is not half of 105 degrees and AB≠AC.
Sorry about that! For some reason, I read ΔBCD as ABCD.
BC = CD = 5√6 ∠CBD = ∠BDC = 45º ∠ADB = 105 - 45 = 60º
BD = 10√3 AD = cos(60º) * 10√3 = 5√3
AC = 16.73