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anonymous

  • 5 years ago

Need help with triangle questions! Please HELP! Find the Area of Triangle ABC. 1. angle b = 25º, a = 10 mm, and c = 15 mm. 2. angle a = 42º, b = 12 cm, and c = 13 cm. 3. angle c = 100º, a = 5 in., and b = 4 in. 4. angle c = 59º, a = 25 ft, and b = 18 ft.

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  1. anonymous
    • 5 years ago
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    are of a triangle is \[\frac{1}{2} ab sin(\theta)\] where \[\theta\] is the measure of the angle between a and b. so these are straightforward i think. first one is \[\frac{1}{2} 10 \times 15 \times sin(25)=31.7\] rounded.

  2. anonymous
    • 5 years ago
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    i am assuming that when you say angle b you mean angle B. commonly lengths are denoted by small letters and the angles opposite them by capitals.

  3. anonymous
    • 5 years ago
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    it this the answer to number 1?

  4. anonymous
    • 5 years ago
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    yes if i used my calculator correctly.

  5. anonymous
    • 5 years ago
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    can you answer the other 3 please? I will give you a good answer for all

  6. anonymous
    • 5 years ago
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    want me to write the next one or do you want to do it. just use the formula.

  7. anonymous
    • 5 years ago
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    you do next one I will do last 2 if I can

  8. anonymous
    • 5 years ago
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    ok here goes: \[\frac{1}{2}\times 12 \times 13 \times sin(42)=52.19\]

  9. anonymous
    • 5 years ago
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    i am just using a calculator. you need one to find the sine of whatever. just make sure it is in "degree" mode. you do one and i will check.

  10. anonymous
    • 5 years ago
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    ok I did 1/2*5*4*sin100 and got -5.063 is that right?

  11. anonymous
    • 5 years ago
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    no you area must be positive.

  12. anonymous
    • 5 years ago
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    i think maybe your calculator is in radian mode. let me check.

  13. anonymous
    • 5 years ago
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    hmmm ok I am using the Ti-84 Plus calc and idk what i did wrong how do I change it?

  14. anonymous
    • 5 years ago
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    hit "mode" and you should see the option there.

  15. anonymous
    • 5 years ago
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    http://answers.yahoo.com/question/index?qid=20090312222055AA3FPqb

  16. anonymous
    • 5 years ago
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    I got 9.84???

  17. anonymous
    • 5 years ago
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    yes!

  18. anonymous
    • 5 years ago
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    wow thanks I get it now!! Can I ask 2 more 1 for each next section then maybe I can understand it!???

  19. anonymous
    • 5 years ago
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    sure ask away.

  20. anonymous
    • 5 years ago
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    sweet thanks

  21. anonymous
    • 5 years ago
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    Find the remaining sides and angles in each triangle. 1. In Triangle ABC , angle M= 38º, a = 20 cm and c = 14 cm.

  22. anonymous
    • 5 years ago
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    i need to know (or rather you need to know) what angle is M? is it opposite a, b or c?

  23. anonymous
    • 5 years ago
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    2. in triangle DEF, d = 24 m, e = 21 m, and f = 25 m. I will try this one Angle m is B

  24. anonymous
    • 5 years ago
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    opposite b? ok

  25. anonymous
    • 5 years ago
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    yeah it say m Angle B=...

  26. anonymous
    • 5 years ago
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    so in the first one you don't know the length of the side opposite angle M = 38 yes?

  27. anonymous
    • 5 years ago
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    yes that sounds right

  28. anonymous
    • 5 years ago
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    because either you are supposed to use the law of sines which says \[\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}\]

  29. anonymous
    • 5 years ago
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    or you are supposed to use the law of cosines which says \[a^2=b^2+c^2-2bc cos(A)\]

  30. anonymous
    • 5 years ago
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    in order to use the first one (which is always easier) you need to know three out of 4 numbers in any one of those ratios. but it looks like in this case you do not. you only know two sides but not the length of the side opposite one of the angles. so you have to use the law of cosines yes?

  31. anonymous
    • 5 years ago
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    yes!

  32. anonymous
    • 5 years ago
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    so we will have to use \[b^2=a^2+c^2 -2ac cos(B)\]

  33. anonymous
    • 5 years ago
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    btw this is easy to remember because it is just pythagoras. if you had a right angle it would be \[c^2=a^2+b^2\] but if it is not a right angle you have to adjust by \[-2ab cos(C)\] ok here goes: \[b^2=20^2+14^2-2\times 20 \times 14 \times cos(38)=154.7\] rounded

  34. anonymous
    • 5 years ago
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    so \[b=\sqrt{154.1}=12.4\] rounded

  35. anonymous
    • 5 years ago
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    at least that is what my calculator told me

  36. anonymous
    • 5 years ago
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    ok lol that makes since

  37. anonymous
    • 5 years ago
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    of course you are not done because you have to find all the rest.

  38. anonymous
    • 5 years ago
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    would it make it easier if I gave you choices? CHoices: b = 12.4 cm2, A = 78.1º, C = 41.5º b = 9.8 cm2, A = 56.1º, C = 57.5º b = 12.4 cm2, A = 98.1º, C = 43.9º b = 12.4 cm2, A = 92.3º, C = 37.6º

  39. anonymous
    • 5 years ago
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    not really. especially since we have only knocked out one answer.

  40. anonymous
    • 5 years ago
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    you still have to find A and C

  41. anonymous
    • 5 years ago
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    oo right ok

  42. anonymous
    • 5 years ago
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    but do not use the law of cosines again, because now you know the side opposite one of the angles. to find angle A use \[\frac{sin(A)}{a}=\frac{sin(B)}{b}\] or \[sin(A)=\frac{a sin(B)}{b}\]

  43. anonymous
    • 5 years ago
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    \[sin(A) = \frac{20 sin(38)}{12.4} = .993\] i think

  44. anonymous
    • 5 years ago
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    damn i am not getting any of your answers.

  45. anonymous
    • 5 years ago
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    sorry....

  46. anonymous
    • 5 years ago
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    ok but i am sure this is correct. we have the 12.4 for sure. now let us find angle C \[\frac{sin(C)}{c}=\frac{sin(B)}{b}\] \[sin(C) = \frac{sin(B)}{b}\] \[sin(C) = \frac{14 sin(38)}{12.4}\] \[C=sin^{-1}(\frac{14 sin(38)}{12.4})\]

  47. anonymous
    • 5 years ago
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    my calc gives 44.03

  48. anonymous
    • 5 years ago
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    but don't forget that we rounded b = 12.4. maybe if we don't round we get a more exact answer.

  49. anonymous
    • 5 years ago
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    yes i get 43.9 if i don't round for b. weird that they would give b as 12.4 but then not round to find A or C.

  50. anonymous
    • 5 years ago
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    ok so A =43.9

  51. anonymous
    • 5 years ago
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    no that was C A you find by subracting: 180 - 38 - 43.9=98.1

  52. anonymous
    • 5 years ago
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    wanna try the next one?

  53. anonymous
    • 5 years ago
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    sryy gotta go thanks for the help tho

  54. anonymous
    • 5 years ago
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    welcome

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