Question

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

Side A = 2
Side B = 8
Side C = 7

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

An obtuse triangle.

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.