Atriangle has side lengths 10, 15, and 7. is the triangle acute, obtuse, or right? show
your work and explain.

Law of cosines:

a²=b²+c²-2.b.c.cos α
a=15
b=10
c=7

Then:

15²=10²+7²-2.(10).(7).cos α
225=100+49-140.cosα
225=149-149.cosα
225-149=-149.cos α
76=-149.cosα
cos α= -76/149

Then:
α=arc cos (-76/149)=120,67º>90º  Then, the triangle is obtuse.

Solution: the triangle is obtuse.