Area of traingle

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  • #1
maxkor
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In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
 

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  • #2
jonah1
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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.
 
  • #3
maxkor
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This is what it looks like, but how to justify the red ones or maybe there is another way?
 

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  • #4
HOI
923
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How did you get those?
 
  • #5
maxkor
90
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Geogebra...
 
  • #6
mrtwhs
48
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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.
 

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