Answer:
An obtuse triangle.
Step-by-step explanation:
We have given the different sides of a triangle that is Side A = 2, Side B = 8 and Side C = 7.
According to the question, we can tell the triangle is acute, obtuse or a right triangle.
We know that,
For given sides x,y,z of a triangle,
If [tex]z^{2}[/tex] = [tex]x^{2} + y^{2}[/tex], then its a right triangle.
If [tex]z^{2}[/tex] < [tex]x^{2} + y^{2}[/tex], then its an acute triangle.
If [tex]z^{2}[/tex] > [tex]x^{2} + y^{2}[/tex], then its an obtuse triangle.
We have a = x = 2, b = z = 8 and c = y = 7.
Note: We always take z as the greatest side length.
Now,
[tex]x^{2} = 4, \ y^{2} = 49, \ and \ z^{2} = 64.[/tex]
We can see that, 4 + 49 < 64.
So, we can apply rule
if [tex]z^{2}[/tex] > [tex]x^{2} + y^{2}[/tex], then its an obtuse triangle.
Therefore,
Given sides are of an obtuse triangle.
