ganeshie8
  • ganeshie8
show that \(a+b=c\) where \(a,b,c\) are the perpendicular distances from vertices to a line passing through the centroid of an equilateral triangle as shown :
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ganeshie8
  • ganeshie8
|dw:1435678656585:dw|
ganeshie8
  • ganeshie8
sorry for the bad drawing credit to @dan815
dan815
  • dan815
|dw:1435679062232:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

dan815
  • dan815
are you sure its true, its seems hard to believe
ganeshie8
  • ganeshie8
Yes it is true, verified with geogebra
dan815
  • dan815
|dw:1435679177952:dw|
ganeshie8
  • ganeshie8
\(a\) and \(b\) need to be on the same side of the line
ganeshie8
  • ganeshie8
|dw:1435679309628:dw|
dan815
  • dan815
oh here is something
dan815
  • dan815
we are dealing with 2 sets of parallel slopes here
TrojanPoem
  • TrojanPoem
Well, c = y sinw , a = y sin ( w - 60) , b = y sin(w +60 ) we have to prove that a + b = c left: a + b = ysin(w-60) + ysin(w+60) = y( sin(w-60)+ sin(w+60)) = y[ sinwcos60 - coswsin60 + sinwcos60 + coswsin60] = y* 2sinwcos60 = ysinw = c
dan815
  • dan815
|dw:1435679496205:dw|
TrojanPoem
  • TrojanPoem
@ganeshie8 , here is the proof. Get the other part from the last question
ganeshie8
  • ganeshie8
that works @TrojanPoem !
dan815
  • dan815
trying to not jump into algebra, wanna see if theres a more pure geometry proof
ganeshie8
  • ganeshie8
exactly ^ there is a really short proof w/o using trig, and looks you had a good start dan
dan815
  • dan815
|dw:1435679888025:dw|
ganeshie8
  • ganeshie8
http://assets.openstudy.com/updates/attachments/558b8754e4b075714118a70e-ganeshie8-1435679847507-zzz.gif
TrojanPoem
  • TrojanPoem
@ganeshie8 , Like++. Nice animation.
dan815
  • dan815
3 sets of similar triangles
dan815
  • dan815
|dw:1435680514378:dw|
dan815
  • dan815
with sides a b a+b
dan815
  • dan815
hey is the motion like a pendulum?
dan815
  • dan815
is that a perfect arc
TrojanPoem
  • TrojanPoem
is think this is a parallelogram with a triangle inscribed
TrojanPoem
  • TrojanPoem
|dw:1435680716273:dw|
dan815
  • dan815
http://prntscr.com/7n5vrt
TrojanPoem
  • TrojanPoem
AC // BD. CD//AB
ganeshie8
  • ganeshie8
wow looks like it, nice imagination dan
dan815
  • dan815
kind of neat haha, if this relationship defined a pedulum motion in a roundabout way
ganeshie8
  • ganeshie8
but it cannot be a circle because the length of that top red segment is changing continuously right
dan815
  • dan815
ya thats true, a calculus solution to this might look interesting too, something to look for later
ganeshie8
  • ganeshie8
yes @TrojanPoem
ganeshie8
  • ganeshie8
let me know if you want me to share my solution because i see now it wont spoil anything as there can be multiple solutions
TrojanPoem
  • TrojanPoem
You gave up guys ?
ganeshie8
  • ganeshie8
nope, we have ur solution so including mine, technically i have 2 solutions... that is far from giving up :D
TrojanPoem
  • TrojanPoem
Come check the new problem, I am stuck with it.
ganeshie8
  • ganeshie8
have you posted it already
ganeshie8
  • ganeshie8
you're right @dan815 the points do trace circles http://gyazo.com/603ef78cc5a38da14adf431b35db870f
TrojanPoem
  • TrojanPoem
I did. But i think it's invisible
ikram002p
  • ikram002p
*

Looking for something else?

Not the answer you are looking for? Search for more explanations.