FibonacciChick666
  • FibonacciChick666
Where does the formula with respect to any triangle \(Area=\frac{1}{2} absin\theta\) come from?
Mathematics
schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
Area of triangle with sides \(\vec{a},~~\vec{b}\) is given by \(\dfrac{1}{2}\vec{a}\times \vec{b}\)
FibonacciChick666
  • FibonacciChick666
I know, but this book is claiming that for any type of triangle the area formula stated above.
jim_thompson5910
  • jim_thompson5910
|dw:1444016348537:dw|

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FibonacciChick666
  • FibonacciChick666
yea that's the rep. if you want the specific Q I can give that to you
jim_thompson5910
  • jim_thompson5910
add in a perpendicular to line 'a', call it h |dw:1444016388804:dw|
jim_thompson5910
  • jim_thompson5910
if we know h, we can compute the area to be a*h/2
jim_thompson5910
  • jim_thompson5910
we can use trig to say sin(theta) = h/b h = b*sin(theta)
jim_thompson5910
  • jim_thompson5910
then do a substitution
FibonacciChick666
  • FibonacciChick666
thank you. It just wasn't happening for me there
jim_thompson5910
  • jim_thompson5910
you're welcome
FibonacciChick666
  • FibonacciChick666
sorry, I more thing. If the angle is obtuse, why does this work?
jim_thompson5910
  • jim_thompson5910
|dw:1444016751760:dw|
FibonacciChick666
  • FibonacciChick666
oh, cause you use 180-theta
jim_thompson5910
  • jim_thompson5910
extend out segment a until it's a line |dw:1444016801093:dw| make sure that the tip is over the line
FibonacciChick666
  • FibonacciChick666
thank you! I'm sorry this test is making me lose my mind
FibonacciChick666
  • FibonacciChick666
(test tomorrow, Praxis)
jim_thompson5910
  • jim_thompson5910
|dw:1444016826079:dw|
jim_thompson5910
  • jim_thompson5910
and i'm sure at this point you can see how sin(180 - theta) = h/b and you can do a bit of manipulation to end up with the same formula
jim_thompson5910
  • jim_thompson5910
good luck on it tomorrow
FibonacciChick666
  • FibonacciChick666
Thanks... I'm just worried. It's been years since most of this stuff
jim_thompson5910
  • jim_thompson5910
http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf idk where on the sheet (if it's even on there), but one identity is sin(pi - x) = sin(x) sin(180 - x) = sin(x)
FibonacciChick666
  • FibonacciChick666
Thanks! Yea, this is the math specific praxis. I'm good on most stuff, but I get really really really bad test anxiety so any extra study material is appreciated!

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