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FibonacciChick666

  • one year ago

Where does the formula with respect to any triangle \(Area=\frac{1}{2} absin\theta\) come from?

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  1. ganeshie8
    • one year ago
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    Area of triangle with sides \(\vec{a},~~\vec{b}\) is given by \(\dfrac{1}{2}\vec{a}\times \vec{b}\)

  2. FibonacciChick666
    • one year ago
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    I know, but this book is claiming that for any type of triangle the area formula stated above.

  3. jim_thompson5910
    • one year ago
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    |dw:1444016348537:dw|

  4. FibonacciChick666
    • one year ago
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    yea that's the rep. if you want the specific Q I can give that to you

  5. jim_thompson5910
    • one year ago
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    add in a perpendicular to line 'a', call it h |dw:1444016388804:dw|

  6. jim_thompson5910
    • one year ago
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    if we know h, we can compute the area to be a*h/2

  7. jim_thompson5910
    • one year ago
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    we can use trig to say sin(theta) = h/b h = b*sin(theta)

  8. jim_thompson5910
    • one year ago
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    then do a substitution

  9. FibonacciChick666
    • one year ago
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    thank you. It just wasn't happening for me there

  10. jim_thompson5910
    • one year ago
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    you're welcome

  11. FibonacciChick666
    • one year ago
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    sorry, I more thing. If the angle is obtuse, why does this work?

  12. jim_thompson5910
    • one year ago
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    |dw:1444016751760:dw|

  13. FibonacciChick666
    • one year ago
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    oh, cause you use 180-theta

  14. jim_thompson5910
    • one year ago
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    extend out segment a until it's a line |dw:1444016801093:dw| make sure that the tip is over the line

  15. FibonacciChick666
    • one year ago
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    thank you! I'm sorry this test is making me lose my mind

  16. FibonacciChick666
    • one year ago
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    (test tomorrow, Praxis)

  17. jim_thompson5910
    • one year ago
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    |dw:1444016826079:dw|

  18. jim_thompson5910
    • one year ago
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    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

  19. jim_thompson5910
    • one year ago
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    good luck on it tomorrow

  20. FibonacciChick666
    • one year ago
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    Thanks... I'm just worried. It's been years since most of this stuff

  21. jim_thompson5910
    • one year ago
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    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)

  22. FibonacciChick666
    • one year ago
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    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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