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anonymous

  • one year ago

an antique map was found in the attic of a local courthouse. it shows some measurements from a local farm that was divided into 5 parts. some of the measurements have faded with age, so you must find the remaining measurements, as well as calculate the total area and perimeter of the outside property. all lengths are measured in miles.

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  1. phi
    • one year ago
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    we need more info. can you make a screen shot of the entire question?

  2. anonymous
    • one year ago
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    how do i do that

  3. anonymous
    • one year ago
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    https://www.georgiastandards.org/Georgia-Standards/Frameworks/Pre-Calculus-Unit-3.pdf

  4. anonymous
    • one year ago
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    the question is on the link but its all the way at the bottom znd it has help on it but i dont understand it

  5. phi
    • one year ago
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    that is a link to 43 pages.

  6. anonymous
    • one year ago
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    you have to scroll all the way down to the bottom

  7. phi
    • one year ago
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    which page?

  8. anonymous
    • one year ago
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    the very last one

  9. anonymous
    • one year ago
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    43

  10. phi
    • one year ago
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    ok. It sounds like they want all the angles and sides for each of the triangles

  11. anonymous
    • one year ago
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    yeah i think so but im not sure how

  12. phi
    • one year ago
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    Mostly the Law of Cosines and Law of Sines Let's start in the lower right. that is a right triangle with sides 3 and 4 use pythagoras to find the hypotenuse.

  13. anonymous
    • one year ago
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    so i would do a^2+b^2=c^2

  14. phi
    • one year ago
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    yes, and we are looking for c

  15. anonymous
    • one year ago
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    4^2+3^2=c^2

  16. anonymous
    • one year ago
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    which equals 25

  17. phi
    • one year ago
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    c^2 = 25 c = sqr(25)

  18. anonymous
    • one year ago
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    5

  19. phi
    • one year ago
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    yes, so label side AC with length 5

  20. anonymous
    • one year ago
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    ok got it

  21. phi
    • one year ago
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    the few pages in front of the last page seem to go through the solution

  22. anonymous
    • one year ago
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    i saw that to but i dont really understand how they did that

  23. phi
    • one year ago
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    Say the job is to find the sides of all 5 triangles. so far you know the sides of triangle ABC

  24. anonymous
    • one year ago
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    ok

  25. phi
    • one year ago
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    now look at triangle ACD. we have two sides and we need to find the 3rd side. Do we have enough info to do that ?

  26. anonymous
    • one year ago
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    we use law of cosine?

  27. phi
    • one year ago
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    yes. If we see side-angle-side with numbers, then we can use the Law of Cosines to find the unknown side. Do you know how to do that to find side AD ?

  28. anonymous
    • one year ago
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    \[5^2+3.1623^2-2(5)(3.1623)\cos(71.5651\]

  29. phi
    • one year ago
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    that is c^2 what do you get for c^2 and then c ?

  30. anonymous
    • one year ago
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    dont you get 35.0-31.623*0.31 and then put that in the calculator?

  31. anonymous
    • one year ago
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    and i got 25.1 but i have to square root it

  32. phi
    • one year ago
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    I would use the calculator to do the whole computation \[ 5^2+3.1623^2-2(5)(3.1623)\cos(71.565)\]

  33. phi
    • one year ago
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    you don't want to round any numbers until the very end.

  34. anonymous
    • one year ago
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    i got 25 still

  35. phi
    • one year ago
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    so what is side AD ?

  36. anonymous
    • one year ago
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    well when i square root 25 i got 5

  37. phi
    • one year ago
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    so label side AD 5 it looks like triangle ACD is isosceles (2 sides the same length) that means we know the base angles are both 71.5651 and the angle CAD is 180 - 2*71.5651 I am not sure we we to write that down, but we do know it.

  38. anonymous
    • one year ago
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    so angle a is the same as angle c (71.5652)

  39. phi
    • one year ago
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    If by angle a and angle c you mean < CDA and < ACD

  40. anonymous
    • one year ago
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    yes

  41. phi
    • one year ago
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    now triangle ADE we have 2 sides, and an angle, but it is the wrong angle. However, we can find the "middle angle". Any ideas how?

  42. anonymous
    • one year ago
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    no i dont know anything about the middle angle

  43. phi
    • one year ago
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    Do you see we want to find side DE ? to do that we can use side AE, angle DAE, side AD and the Law of Cosines but we need angle DAE

  44. phi
    • one year ago
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    When I see we have sides and angles, and need an angle, I would try using the Law of Sines. What angle can we find if we use the Law of Sines ?

  45. anonymous
    • one year ago
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    \[cosc=a^2+b^2-c^2/2ab\]

  46. phi
    • one year ago
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    we can't use that because we don't know two things (angle C and side c) I would use the Law of Sines to find angle ADE

  47. anonymous
    • one year ago
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    so then sin=a/sinA=b/sinB

  48. phi
    • one year ago
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    yes. can you find angle ADE ?

  49. anonymous
    • one year ago
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    remind me again is the a the side and the A is the degree right

  50. phi
    • one year ago
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    yes, you can only take sines of angles. you can write the Law of Sines as \[ \frac{a}{\sin A} = \frac{b}{\sin B}\] or as \[ \frac{\sin A}{a} = \frac{\sin B}{b}\]

  51. anonymous
    • one year ago
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    ok \[\sin=\frac{ 7.8102 }{ sinA }=\frac{ 5 }{ \sin38.845 }\]

  52. phi
    • one year ago
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    ok except I would not have that first sin = part just \[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.845 }\]

  53. phi
    • one year ago
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    typo: \[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.8845 } \]

  54. anonymous
    • one year ago
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    oh ok and then sin(38.845 is equal to 0.62 so you have \[\frac{ 7.8102 }{ ?sinA}=\frac{ 5 }{ 0.62 }\]

  55. phi
    • one year ago
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    it's sin 38.8845 (not 38.845) when you do the calculation you should keep at least 5 decimals (I would keep all that the calculator uses)

  56. anonymous
    • one year ago
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    0.6277524996

  57. phi
    • one year ago
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    The way I would do it is write it as \[ \frac{\sin A}{7.8102} = \frac{\sin 38.8845}{5} \] and then multiply both sides by 7.8102 to get \[ \sin A =\frac{\sin 38.8845}{5}\cdot 7.8102\] now use a calculator to find sin A

  58. anonymous
    • one year ago
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    i put that in and it says error

  59. phi
    • one year ago
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    you can use google. type into the google search window sin 38.8845 deg * 7.8102/5=

  60. anonymous
    • one year ago
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    okay thank you for everything i got the rest your the best

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