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09.01.2020

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 $z^{2}$ = $x^{2} + y^{2}$ , then its a right triangle.

If $z^{2}$ < $x^{2} + y^{2}$ , then its an acute triangle.

If $z^{2}$ > $x^{2} + y^{2}$ , 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,

$x^{2} = 4, \ y^{2} = 49, \ and \ z^{2} = 64.$

We can see that, 4 + 49 < 64.

So, we can apply rule

if $z^{2}$ > $x^{2} + y^{2}$ , then its an obtuse triangle.

Therefore,

Given sides are of an obtuse triangle.

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