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# Analytic geo, perhaps?

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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:

https://ibb.co/1GfxMNx

Dec 18, 2020

#1
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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)

Dec 18, 2020
#2
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Please be careful when you are answering, ABD is not half of 105 degrees and AB≠AC.

Dec 18, 2020
edited by Pangolin14  Dec 18, 2020
edited by Pangolin14  Dec 18, 2020
edited by Pangolin14  Dec 18, 2020
#4
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = CD = 5√6          ∠CBD = ∠BDC = 45º          ∠ADB = 105 - 45 = 60º

BD = 10√3            AD = cos(60º) * 10√3 = 5√3

AC = 16.73

jugoslav  Dec 18, 2020
edited by jugoslav  Dec 18, 2020
edited by jugoslav  Dec 18, 2020
#5
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Thanks! Exactly what I got!

Pangolin14  Dec 20, 2020
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Angle CBA =75 degrees
Angle CBD =45 degrees
Angle DBA =30 degrees

By Pythagoras