Answer:
acute, because 10²+12²>15²
Step-by-step explanation:
You want to classify a triangle with sides 10 in, 12 in, and 15 in.
The "form factor" (f) of the triangle can be computed as ...
f = a² +b² -c²
where a, b, c are the side lengths in increasing order. This is positive for an acute triangle, negative for an obtuse triangle, and zero for a right triangle.
f = 10² +12² -15² = 100 +144 -225 = 19
f > 0
That is to say 10² +12² > 15², so the triangle is acute
__
Additional comment
The largest angle in the triangle is arccos(f/(2ab)). In this triangle, that is ...
arccos(19/(2·10·12)) ≈ 85.46°, an acute angle