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January 4th, 2014, 01:56 PM   #1
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Rhombus.

ABCD is Rhombus. Measuring the angle (A)=40
Point m belongs to the segment AD
Measuring the angle (m BD)=30
find Measuring the angle mCD
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January 4th, 2014, 07:42 PM   #2
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It's easy to show that it's 10 by using trigonometry.

A geometrical proof is achievable, based on the diagram below.

[attachment=0:28nbddm5]Rhombus.gif[/attachment:28nbddm5]
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File Type: gif Rhombus.gif (2.8 KB, 78 views)
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January 4th, 2014, 10:26 PM   #3
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Re: Rhombus.

can you send the by using trigonometry. solve
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January 4th, 2014, 11:00 PM   #4
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Re: Rhombus.

Nice one Skip! I got to angleDCM = angleBMC - 40, but tires started spinning at that point...

Quote:
Originally Posted by mared
can you send the by using trigonometry. solve
Well, maybe someone will type out the whole solution for you, but not me...
I can supply a hint if YOU're willing to do some work:
let the side lengths = 1
then, since triangle ABM is isosceles and angleAMB = 100, then AM = BM = .5 / SIN(50)
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January 5th, 2014, 05:41 AM   #5
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Further hint: using .5 = sin(30),
MD = 1 - BM = (sin(50) - sin(30))/sin(50) = 2cos(40)sin(10)/sin(50) = 2sin(10).
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