Question

Using the side lengths, determine whether the triangle is acute, obtuse, or right.

Answer 1

The answer is acute this is because if there is two longer sides and a short side that makes the triangle acute

Answer 2

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 $z^{2}$ = $x^{2} + y^{2}$, 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.