Which best explains whether a triangle with side lengths 2 in, 5in, and 4 in is an acute triangle

For an acute angled triangle
a^2 < b^2 + c^2   where a is the longest side

so here  we have:-

5^2  = 25

4^2 + 2^2 = 16 + 4 =  20

so 5^2 > 2^2 + 4^2   so this triangle is not acute.   It is obtuse.

In summary  

a^2 < b^2 + c^2  = acute angled

a^2 = b^2 + c^2 = right angled

a^2 > b^2 + c^2 = obtuse angled triangle.