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Up to a trigonometry puzzle ?

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  1. #1

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    Up to a trigonometry puzzle ?

    Ok so my daughter has this puzzle as part of an assignment in math...
    The original puzzle is a bit more complex involving... a goat (don't ask) but I reduced it to the below: calculate the area in red color.
    Inner circle has a radius of 3cm.
    Outer circle has a radius of 4cm.
    One important piece of information is that we are not allowed to express angles as a fraction of Pi.

    I'm frustrated .


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    @cendrillon

    imparanoic likes this.

  2. #2

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    Is this a variation of one of those box in a circle problems and is the answer 5.56cm^2?

    Where you use Pythagoras and take 4^2 - 3^2 and you get 7^0.5 and solve that the area of the (imaginary) box is 28 then subtract from the circle with a 4 cm radius to get an area of 50.24 (3.14*4^2) then take the resulting figure of 22.24 and divide by 4?


  3. #3

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    If the area is 3.63cm.sq, you can try calculating the area of segment from area of sector minus area of triangle. For area of sector, u need the angle, which u can get thru Pythagoras principle.


  4. #4

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    You beat me to it @shafiq - I got the same result as you 3.628

    https://www.mathopenref.com/segmentarea.html


  5. #5

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    Apologies I should have mentioned as well that my daughter hasn't learnt sin/cos yet.
    @Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

    Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

    It's one of those puzzles where you need a good pair of eyes more than a brain.

    (3.14x4^2 - 3^2)/4=10.31

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    Last edited by jrkob; 17-09-2019 at 09:53 AM.

  6. #6

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    Quote Originally Posted by jrkob
    Apologies I should have mentioned as well that my daughter hasn't learn sin/cos yet.
    @Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

    Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

    It's one of those puzzles where you need a good pair of eyes more than a brain.

    (3.14x4^2 - 3^2)/4=10.31

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    This will be stored in case something like it comes up in my kids' homework and I can then impress them with my intelligence!
    chuckster007 and Sith like this.

  7. #7

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    Quote Originally Posted by jrkob
    Apologies I should have mentioned as well that my daughter hasn't learnt sin/cos yet.
    @Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

    Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

    It's one of those puzzles where you need a good pair of eyes more than a brain.

    (3.14x4^2 - 3^2)/4=10.31

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    Side of square is 6 or 3?.
    Area should be 3.6 either way?
    shri likes this.

  8. #8

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    Outer circle - Pi x 4 x 4 = 50.24
    Inner Square - 6x6 = 36
    Arc = (50.24-36)/4 = 3.56 = 3.6

    rkenia852 likes this.

  9. #9

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    Oops yes I posted a bit quick and before my first coffee.
    3.6
    @hullexile I'll post the entire worksheet tonight when I'm home. The puzzles then get more complicated

    hullexile likes this.

  10. #10

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    I'm only here for the goat


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