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area of traingle

maxkor

Member
Jul 22, 2014
62
In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
 

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jonah

Active member
Feb 21, 2015
109
Beer induced request follows.
In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
Please show us what you have tried and exactly where you are stuck.
We can't help you if we don't where you are stuck.
 

maxkor

Member
Jul 22, 2014
62
This is what it looks like, but how to justify the red ones or maybe there is another way?
 

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Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
854
How did you get those?
 

maxkor

Member
Jul 22, 2014
62
Geogebra...
 

mrtwhs

Active member
Oct 15, 2015
45
In your diagram, all three sides of $\triangle AEC$ are known. Using the law of cosines you get $2\alpha = \cos^{-1}(7/8)$ and $\alpha \approx 14.47751219^{\circ}$.

Continuing to use the law of cosines we get $AD=\dfrac{3\sqrt{10}}{2}$ and $AB=3\sqrt{6}$.

Finally, using the law of cosines on $\triangle ABD$ we get $\alpha \approx 71.170769^{\circ}$.

Your diagram is incorrect.