Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

BecomeMyFan=D Group Title

One corner of a triangle has a 60° angle and the length of the two adjacent sides are in ratio 1 : 3. Calculate the angles of the other triangle corners (0,1°:s precision, 1 point / correct angle).

  • 3 years ago
  • 3 years ago

  • This Question is Closed
  1. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :)

    • 3 years ago
  2. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think I have to first find the size of the opposite side to 60 degree angle right? i used cosine rule to do so and found 2.65, however I dont know what to do now

    • 3 years ago
  3. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    2.645, not 2.65

    • 3 years ago
  4. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, you're on the right track. Now use sine rule to find your angles...but, note you only have to use it once because the sum of the angles of a plane triangle is 180 degrees (and by the time you apply the sine rule, you'll have two of them).

    • 3 years ago
  5. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, so then I just sub the 2 angs form 180 and.... right?

    • 3 years ago
  6. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    First find one of the other angles.

    • 3 years ago
  7. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I just did

    • 3 years ago
  8. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    79.2

    • 3 years ago
  9. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    something is not right

    • 3 years ago
  10. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think you found the sum of 60 and one of the other ones, 19.1.

    • 3 years ago
  11. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    is 2.645 right for the third side?

    • 3 years ago
  12. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{a}{\sin \theta}=\frac{\sqrt{7} a}{\sin 60^o}\]

    • 3 years ago
  13. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i found one angle to be 19.1

    • 3 years ago
  14. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Your third side is right, assuming, in your ratio of 1:3, the side with the '1' has unit length. A more general assumption is that this side has length 'a', so that the other side has length 3a.

    • 3 years ago
  15. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The side opposite 60 degrees would then have length,\[\sqrt{7}a\]

    • 3 years ago
  16. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, you're right.

    • 3 years ago
  17. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how?

    • 3 years ago
  18. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, yeah, i get it

    • 3 years ago
  19. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    How? Cosine rule, like you used before (if you're asking how I get sqrt(7)a?).

    • 3 years ago
  20. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Once the other angle's found, you're done.

    • 3 years ago
  21. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, subing 19.1+60 from 180 gives 100.9

    • 3 years ago
  22. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but

    • 3 years ago
  23. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    when i try to find the last angle using sine rule, it gives me 79.2

    • 3 years ago
  24. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    which is right?

    • 3 years ago
  25. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, you're right...

    • 3 years ago
  26. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i did something wrong then

    • 3 years ago
  27. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Bizarre

    • 3 years ago
  28. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :)

    • 3 years ago
  29. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    In mathematics, if you end up with a contradiction, it's because one of your assumptions is wrong...so what assumption(s) were made?

    • 3 years ago
  30. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the ratio of sides 1 to 3, the sine rule, the cosine rule and the 60 angle

    • 3 years ago
  31. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Does your question say "the length of *the* two adjacent sides" or "the length of two adjacent sides"?

    • 3 years ago
  32. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the

    • 3 years ago
  33. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    whats the difference?

    • 3 years ago
  34. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    'the' restricts your choice

    • 3 years ago
  35. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it says adjacent

    • 3 years ago
  36. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but i still dont see what I did wrong :(

    • 3 years ago
  37. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Omg, it just dawned on me - there are two possible solutions!

    • 3 years ago
  38. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    One set will have (60, 9.1 and the other) and (60, 79.2, other)

    • 3 years ago
  39. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    One assumption was missed - that there is only one solution.

    • 3 years ago
  40. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I constructed a triangle on the description in GeoGebra and have (60,9.1,100.9) as one solution.

    • 3 years ago
  41. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :) so there is just one solution?

    • 3 years ago
  42. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    No, it's coming about because the arc of sine (in on rotation) has TWO angles whose sine is positive and the same value.

    • 3 years ago
  43. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    in *one* rotation

    • 3 years ago
  44. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so, is it then imposible to find both of the angles correctly?

    • 3 years ago
  45. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    No, it's just that you collect both possible solutions from the arc of sine on each angle, and then put them in the appropriate combinations (i.e. so they add to 180).

    • 3 years ago
  46. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so, how do I answer the quesstion in a work book? which set of angles do I choose?

    • 3 years ago
  47. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok..I'm trying to figure out a way to do it so that it doesn't take a millennium to type.

    • 3 years ago
  48. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wouldn't the other angle be 30 and the other 90?

    • 3 years ago
  49. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    since the other is 60?

    • 3 years ago
  50. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{\sin \alpha}{3a}=\frac{\sin 60}{\sqrt{7}a}\rightarrow \sin \alpha = \frac{3\sqrt{3}}{2\sqrt{7}}\]

    • 3 years ago
  51. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Now

    • 3 years ago
  52. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    in the arc of 360 degrees, \[\alpha = \sin^{-1}\frac{3\sqrt{3}}{2\sqrt{7}}\] degrees AND\[\alpha = 180- \sin^{-1}\frac{3\sqrt{3}}{2\sqrt{7}}\]

    • 3 years ago
  53. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    where \[\sin^{-1}\frac{3\sqrt{3}}{2\sqrt{7}}\approx 79.1^o\]

    • 3 years ago
  54. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So the possible angles you get as solutions when considering this combination of sides is\[79.1^o, 100.9^o\]

    • 3 years ago
  55. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Try taking the sine of both of them in your calculator.

    • 3 years ago
  56. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So you have NO CHOICE but to accept two solutions for this first combination of sides.

    • 3 years ago
  57. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I get it

    • 3 years ago
  58. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    THANKS ALOT

    • 3 years ago
  59. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hang on...

    • 3 years ago
  60. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

    • 3 years ago
  61. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    just one question, is it a right triangle? ^_^

    • 3 years ago
  62. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the question does not specify

    • 3 years ago
  63. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    because if so, then the other 2 angles are 90 and 30, otherwise , loki's answer is true :)

    • 3 years ago
  64. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Wait wait wait...

    • 3 years ago
  65. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :)

    • 3 years ago
  66. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    When you take the arc of sine here you'll get two solutions for each angle, which are algebraically correct.

    • 3 years ago
  67. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    lol, alright

    • 3 years ago
  68. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So, calling those angles alpha and beta, you have\[\alpha \in \left\{ 79.1,100.9 \right\}\]and\[\beta \in \left\{ 19.1, 160.9 \right\}\]

    • 3 years ago
  69. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    BUT

    • 3 years ago
  70. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    only certain combinations of those angles will give you a true conclusion here, since you have an additional constraint: that the angles\[\alpha, \beta, 60^o\]must sum to 180 degrees.

    • 3 years ago
  71. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So you have to find those combinations elements from the set of alpha and beta that will allow you to get 180 (after you add 60 to them). You see?

    • 3 years ago
  72. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    then alpha is 100.9 and beta is 19.1 ?

    • 3 years ago
  73. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    There are four possible combinations, but only ONE combination works

    • 3 years ago
  74. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

    • 3 years ago
  75. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and he strikes again~ lol

    • 3 years ago
  76. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and i;m drunk - came back from a dinner

    • 3 years ago
  77. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but you've answered it , weirdly in such a state ._. did you get it andy?

    • 3 years ago
  78. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It's similar to a situation when you have to solve the quadratic equation, which might have something to do with length, and you get two solutions - one positive, one negative. You apply an additional constraint (i.e. physical measurements aren't negative) and discard one of the solutions. Here, the constraint is that you can only take those angles whose sum will be 180.

    • 3 years ago
  79. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • 3 years ago
  80. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and, lokisan, you dont sound like drunk

    • 3 years ago
  81. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe half drunk ~

    • 3 years ago
  82. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\left\{ \alpha, \beta|\alpha + \beta +60^o=180^o , \alpha \in \left\{ 79.1,100.9 \right\},\beta \in \left\{ 19.1,160.9 \right\} \right\}\]

    • 3 years ago
  83. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    discrete mathematics ^^" ...

    • 3 years ago
  84. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes...so the above set is 19.1 and 100.9.

    • 3 years ago
  85. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Phew

    • 3 years ago
  86. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Good question.

    • 3 years ago
  87. sstarica Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    LOL

    • 3 years ago
  88. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Happy with that BMFan?

    • 3 years ago
  89. BecomeMyFan=D Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, it is hard, but i am damn happy

    • 3 years ago
  90. lokisan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome

    • 3 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.