Classify by angle the triangle whose side lengths are square root 48, square root 22, and 4

Answer 1

48 > 22 + 16

48>38

It's an obtuse triangle

(sqr48)^2 = (sqr22)^2 + 4^2

48> 22 +16 = 38

48>38

but you may also want to check to see if

sqr48<sqr22+4

about

6.9<8.7 which is ok.

if the inequality were reversed, it's not a triangle at all

or speaking loosely it's so obtuse, it's not a triangle.

the longest side can't be greater than the sum of the other two sides

Answer 2

Try the Pythagorean Theorem. Square the two smaller sides (4 and √22) and see if their sum is greater than, equal to, or less than the square of the largest side (√48):

1. If a² + b² = c², the triangle is a right triangle
2. If a² + b² < c², the triangle is obtuse
3. If a² + b² > c², the triangle is acute