80 degrees

apple2357

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Can anyone help me see why ACB is 80 degrees?

I have tried playing with parallel lines and basic ideas of geometry and some similar triangles stuff.
Any hint please?
 

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Can anyone help me see why ACB is 80 degrees?

I have tried playing with parallel lines and basic ideas of geometry and some similar triangles stuff.
Any hint please?
WHO says angleACB = 80 degrees?

I get 80.4426.... (close but no ceegar...)

Did you use the Law of Sines?

Can you supply a fully labelled diagram?
 
WHO says angleACB = 80 degrees?

I get 80.4426.... (close but no ceegar...)

Did you use the Law of Sines?

Can you supply a fully labelled diagram?

The claim is correct; I've verified it with trig. Essentially, the claim is that tan 50 + tan 60 + tan 70 = tan 80, which is exactly true.

I've also seen some problems with similar angles that can be shown to be exact using rather complicated geometry.

I'm working on making the trig demonstrate that the answer is exact, but it would be nice to find a purely geometrical approach.
 
Can anyone help me see why ACB is 80 degrees?

I have tried playing with parallel lines and basic ideas of geometry and some similar triangles stuff.
Any hint please?

Are we to assume \(\displaystyle \overline{AB}\parallel\overline{(Unlabled)C}\)?
 
As I'm interpreting it, ABC[D] is a rectangle, and the broken lines are both parallel to BC. Of course, all this should really have been stated.

Indeed. I was still wondering if AB was a line or a three segment path. Please state clearly what intended.
 
Changing it a bit.....

Code:
D          E                                         C


1                                                    1

  
A                        F                           B 

Rectangle ABCD, AD = BC = 1. E on CD, F on AB.

angleDAE = 50, angleCEF = 30, angleBFC = 20
Calculate angle ACB

We all agree??!!
 
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Can anyone help me see why ACB is 80 degrees?

I have tried playing with parallel lines and basic ideas of geometry and some similar triangles stuff.
Any hint please?
Angle

Is it easier to show that \(\displaystyle \overline{CA}\;bisects\;\angle{ECF}\)? <== It's really annoying when it works in the preview and then fails in the posting.

And why would that be interesting?
 

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@tkhunny: The question about the LaTeX code failing was recently posted. The word "angle" automatically connects to a link which screws up the LaTeX. If you put the word (angle) into text before the LaTeX code it will work. For example you could have said the following:

Is it easier to show that the angle \(\displaystyle \overline{CA}\;bisects\;\angle{ECF}\)?

-Dan
 
@tkhunny: The question about the LaTeX code failing was recently posted. The word "angle" automatically connects to a link which screws up the LaTeX. If you put the word (angle) into text before the LaTeX code it will work. For example you could have said the following:

Is it easier to show that the angle \(\displaystyle \overline{CA}\;bisects\;\angle{ECF}\)?

-Dan

Kinda random. Thanks :)
 
Rectangle ABCD, AD = BC = 1. E on CD, F on AB.
angleDAE = 50, angleEFG = 60, angleCFG = 70

Code:
D          E             G                           C


1                        1                           1

  
A                        F                           B
F..K!! I was getting 80.4426...due to a moronic goof:
triangle EFG being 30-60-90, then EF = 2,
but I assigned the "2" to EG:x

Solution (as per DocP again!):
DE = tan(50) = 1.191754...
EG = tan(60) = 1.732051...
GC = tan(70) = 2.747477...

Makes CD = 5.671282...
resulting in angleACD = 10, thus angleACB = 80.

Yessss......I'm already in the corner.....!!
 
Yessss......I'm already in the corner.....!!
I think you like being in the corner!

There was once a mother who cleaned out her teen son's room one day and found a cache of whips, chains, and bondage videos. She asked her husband what to do about it and he replied "Well I wouldn't spank him."

-Dan
 
There was once a mother who cleaned out her teen son's room one day and found a cache of whips, chains, and bondage videos. She asked her husband what to do about it and he replied "Well I wouldn't spank him."
-Dan
:p
 
Kinda random …
A number of vBulletin bugs act that way. Yet, the conflict between autolinking and LaTeX keywords is consistent. (The site doesn't apply autolinking in previews, so the issue doesn't show up until posting.)

In other words, when our post contains LaTeX, we need to proof our typing twice: once in preview (overall), and then again (just the LaTeX renderings) after posting. Problems with LaTeX code are usually highlighted in red, but also be mindful of hyperlinks in the unrendered code (they appear in blue). :cool:
 
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