Question

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

Answer 1

@Jack1

Answer 2

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

Answer 3

so it is a?

Answer 4

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 ?

Answer 5

yup so then it is more than 2 correct?

Answer 6

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

Answer 7

alrighty thxs

Answer 8

np man ;)

Answer 9

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

Answer 10

90 and 30 will NOT count, as one of the angles is obtuse, that is GREATER than 90 and LESS than 180