Answer:
Acute.
Step-by-step explanation:
Using the Triangle Inequality Theorem you know that the sum of the lengths of two sides of a triangle are greater than the length of the third side.
Using this we can narrow it down that this DOES have a solution, since 10+12>15.
Now, we can determine if this triangle is a right triangle using the Pythagorean Theorem. C is the longest length.
If c^2= a^2+b^2, then it is a right triangle.
If c^2< a^2+b^2 then it is an acute triangle.
If c^2>a^2+b^2 then it is an obtuse triangle.
We can now substitute. (A and B are interchangeable, but C is the longest length.
A=10
B=12
C=15
A^2=100
B^2=144
C^2=255
We can now figure out that this triangle is acute because A^2+ B^2 (244) < C^2 (255).
Hope this helps!
