## 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

1. OregonDuck

@Jack1

2. Jack1

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

so it is a?

4. Jack1

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

yup so then it is more than 2 correct?

6. Jack1

yeps, about 30 possibilities if u only go for whole numbers

7. OregonDuck

alrighty thxs

8. Jack1

np man ;)

9. anonymous

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

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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