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MCIII Geo 3.16, 3.12

 
 
Picture of Tina Jin
MCIII Geo 3.16, 3.12
by Tina Jin - Tuesday, January 30, 2024, 5:53 PM
 

Hello,

I need some help with these questions.

3.12: I don't know how to start

3.16: I divided the right part of the trapezoid into a 30-60-90 triangle and calculated the height, but I don't know how to solve it from there. I tried extending the sides BA and CD, and I tried using the area  (it led to an identity), and I don't know the cos(50) or otherwise I would've used that to solve the problem.

Thanks,

Tina Jin

 
Picture of Dr. Kevin Wang
Re: MCIII Geo 3.16, 3.12
by Dr. Kevin Wang - Tuesday, January 30, 2024, 6:10 PM
 

3.16 is not a hard problem, if you slow down and think about it :)  I don't think there is 30-60-90 triangle.  Try to draw a line through A that is parallel to line CD.


 
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Picture of Dr. Kevin Wang
Re: MCIII Geo 3.16, 3.12
by Dr. Kevin Wang - Tuesday, January 30, 2024, 6:24 PM
 

Full solution for 3.12 is here.  It requires a few steps of area transformation.



 
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