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OregonDuck

  • one year ago

How many unique triangles can be made where one angle measures 60° and another angle is an obtuse angle? 1 2 More than 2 None

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  1. OregonDuck
    • one year ago
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    @Jack1

  2. Jack1
    • one year ago
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    obtuse = more than a right angle but less than 180 degrees so 1 angle = between 90 and 180 and 1 angle = 60 and a triangle's angles add up to 180

  3. OregonDuck
    • one year ago
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    so it is a?

  4. Jack1
    • one year ago
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    so 180 - 60 = 120 so all obtuse angles between 90 and 119 will work for the other 2 angles, yeah? ie 90 and 30 91 and 29 92 and 28 93 and 27... etc? u sensing the pattern man ?

  5. OregonDuck
    • one year ago
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    yup so then it is more than 2 correct?

  6. Jack1
    • one year ago
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    yeps, about 30 possibilities if u only go for whole numbers

  7. OregonDuck
    • one year ago
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    alrighty thxs

  8. Jack1
    • one year ago
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    np man ;)

  9. anonymous
    • one year ago
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    The third angle is fixed at 60 degrees, so the remaining angles must add up to 120, let the obtuse angle be x, then clearly we have \[(x,120-x)\space, \space x \in \left\{ 91,92,93,...,119 \right\}\] That's definitely more than 2

  10. anonymous
    • one year ago
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    90 and 30 will NOT count, as one of the angles is obtuse, that is GREATER than 90 and LESS than 180

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