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Math Help - Radions, Circles, Arcs

  1. #1
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    Radions, Circles, Arcs

    This is a question I did about 4 times and kept getting a weird answer. I feel like I know where the mess up just because of the obscenely large number but I don't know what the mess up IS.

    Okay here is it.

    Two circles, each of radius 14 cm, are drawn with their centres 20 cm apart. Find the length of their common chord. Find also the area common to the two circles.

    Okay I found the common chord which is 19.6 cm.

    So to find the area common to the two circles, I first find that area of the sector and then I find the area of the triangle formed with the chord and subtract the latter from the former.

    THIS IS WHERE I BELIEVE MY MESSUP IS.

    To find the area of the sector, the formula is (1/2)(r^2)(theta)

    So I gotta find theta.

    I use the triangle formed by the chord to find theta. I divide that triangle into 2 so that it is a right angled triangle and so that I can use SOHCAHTOA.


    sintheta=opp/hyp
    sintheta=9.8/14
    theta=inverse sin(9.8/14)

    (9.8 is the chord length divided by 2)

    I get 44.41. I multiply that by 2. and I have what I presume is the accurate angle. I insert this all into the equation.

    (1/2)(14^2)(88.8)
    = 8704.36

    WHAAAAAT? Okay that has to be wrong but I don't know how/where?

    Finding the area of the triangle formed by chord:
    base * height / 2
    = 19.6*10 / 2
    = 98
    Nice looking number - looks accurate.

    The answer to this question is 108 cm^2.
    So the area of the sector is definetely wrong. Please help me found out where?
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  2. #2
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    You need to use radians, not degrees for the angle. The area of sector 1/2rētheta only works with radians.
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  3. #3
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    oops sorry
    Last edited by juliak; November 9th 2009 at 03:04 AM. Reason: realized the stupidity of my question after i posted it
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  4. #4
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    Oh. Um I converted 88.3 to radians by multiplying it by pi/180

    I got 1.54

    so .5*15^2*1.54 = 151.03

    151.03 0- 98 (area of chord formed with triangle) = 53 cm^2

    That's not right either :S
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