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anonymous

  • 5 years ago

Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters. The length of the chord AB is 6 centimeters. Answer to 2 decimal places. (Hint: Triangle ABC is a right triangle.) put in cm^2 http://www.webassign.net/sat/10-4-29.gif

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  1. anonymous
    • 5 years ago
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    Several ways to this, higher math use double integrals polar. However, it could be done geometrically. Calculate the area of the triangle; calculate area of semi-circle; Subtract

  2. amistre64
    • 5 years ago
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    this one right?

  3. anonymous
    • 5 years ago
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    yup

  4. amistre64
    • 5 years ago
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    ah, thats such a pretty picture lol

  5. anonymous
    • 5 years ago
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    haha lol. its 3am and im doin maths lol. thats commiitment haha

  6. amistre64
    • 5 years ago
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    diam = 8; radius = 4 the area of each 'segment' = area sector - area triangle

  7. amistre64
    • 5 years ago
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    lets get the larger angle; using law of cos; in a good way lol 6^2 = 4^2 + 4^2 - 2(4)(4) cos(C) 36 - 16 - 16 ----------- = cosC; C = cos^-1 of that stuff right? -32

  8. amistre64
    • 5 years ago
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    36 - 32 = 4 -4 --- = -1/8 32

  9. anonymous
    • 5 years ago
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    haha looks good

  10. anonymous
    • 5 years ago
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    -1/8 ill giv it a try

  11. amistre64
    • 5 years ago
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    151.04 is what i get in degrees lol

  12. amistre64
    • 5 years ago
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    2.636 rads i think

  13. anonymous
    • 5 years ago
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    hahaha. so im guessin the -1/8 is in cm^2 ?

  14. amistre64
    • 5 years ago
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    ..... maybe :)

  15. anonymous
    • 5 years ago
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    hahahaha

  16. amistre64
    • 5 years ago
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    there is a simpler way.... my other personality just was sitting there laughing at me and finally told me this..

  17. amistre64
    • 5 years ago
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    since the radius = 4; what is the area of the half cirlce? pi r^2 ----- right? 2

  18. anonymous
    • 5 years ago
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    righto

  19. amistre64
    • 5 years ago
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    8pi total area of the half....

  20. amistre64
    • 5 years ago
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    subtract area of the tri now

  21. anonymous
    • 5 years ago
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    ohh i see. and area of tri is found by cos formula right?

  22. amistre64
    • 5 years ago
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    or vectors :)

  23. amistre64
    • 5 years ago
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    but yeah

  24. anonymous
    • 5 years ago
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    how do u use vectors

  25. amistre64
    • 5 years ago
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    draw lines with arrows attached

  26. amistre64
    • 5 years ago
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    lets go with law of cosines to figure angles tho

  27. anonymous
    • 5 years ago
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    area triangle (1/2)bh

  28. amistre64
    • 5 years ago
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    to find the height we gotta know an angle

  29. anonymous
    • 5 years ago
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    Height is given, right triangle.

  30. amistre64
    • 5 years ago
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    cos^(-1)[-1/8] gives us an inside angle of what... 115.yada right?

  31. amistre64
    • 5 years ago
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    151.04497562814015224245793040175 i meant lol

  32. amistre64
    • 5 years ago
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    180 - angle ---------- = angle we can use 2

  33. anonymous
    • 5 years ago
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    i got 97.180

  34. amistre64
    • 5 years ago
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    14.477512 is the angle onthe left side

  35. amistre64
    • 5 years ago
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    6 sin(angle) = height

  36. anonymous
    • 5 years ago
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    kinda lost me there

  37. amistre64
    • 5 years ago
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    the interior angle at the center there is abt 151 right?

  38. anonymous
    • 5 years ago
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    ye i was gettin about 97.18 instead of the 151

  39. amistre64
    • 5 years ago
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    we got an isosoleces triangle so the other 2 angles are the same right? 180 - 151 --------- = angle we need 2

  40. amistre64
    • 5 years ago
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    why do i get dofferent result lol

  41. amistre64
    • 5 years ago
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    it is -1/8 right?

  42. anonymous
    • 5 years ago
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    lol not sure but is it cos(^-1)(-1/8) ?

  43. anonymous
    • 5 years ago
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    yeah,, the -1/8 part cud be the mess up

  44. amistre64
    • 5 years ago
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    6^2 = 4^2+4^2 -2(4)(4) cosC 36 - 32 ------- = 4/-32 = -1/8 -32

  45. anonymous
    • 5 years ago
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    nah it cant be then

  46. amistre64
    • 5 years ago
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    cos^-1(-1/8) = abt. 97

  47. anonymous
    • 5 years ago
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    yes thats the one

  48. amistre64
    • 5 years ago
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    it must be my fat fingers gettin gin the way lol

  49. anonymous
    • 5 years ago
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    hahaha its all good

  50. amistre64
    • 5 years ago
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    180 - 97.180755781458281323038995626149 -------- 2

  51. amistre64
    • 5 years ago
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    41.409622109270859338480502186926 now we got this angle we can determine the height by its sin times that 6 distance

  52. amistre64
    • 5 years ago
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    3.968... is what I get for height

  53. amistre64
    • 5 years ago
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    h*8 --- = area of tri 2

  54. anonymous
    • 5 years ago
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    lol for the height i got -0.92

  55. amistre64
    • 5 years ago
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    15.8745 = area tri now subtract that from the area of the hemicircle

  56. amistre64
    • 5 years ago
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    lol.... do it again

  57. anonymous
    • 5 years ago
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    so u did Sin(41.40*6) for height?

  58. amistre64
    • 5 years ago
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    8pi - 15.8745.... = 9.258....

  59. amistre64
    • 5 years ago
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    the 6 is outside

  60. amistre64
    • 5 years ago
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    6 sin(angle)

  61. anonymous
    • 5 years ago
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    ohhh

  62. anonymous
    • 5 years ago
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    okah so its 9.258 cm^2

  63. amistre64
    • 5 years ago
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    thats what i get; but then again.... i am just an idiot in disguise ;)

  64. anonymous
    • 5 years ago
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    lol as if. u answered so many of my q's!!!

  65. anonymous
    • 5 years ago
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    and wallah its correct!!

  66. amistre64
    • 5 years ago
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    yay!!

  67. anonymous
    • 5 years ago
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    double yay!!!

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