Tell whether the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

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Tell whether the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

15, 18, 20

and

7, 8, 11

and

6, 7, 3(times the square root of 13)

We know that in a right angled triangle , the greatest side is hypotenuse.

So if ABC is a right angled triangle with a right angle at B, then the greatest side is the hopetenuse AC .

Therefore AC^2 = AB^2+BC^2.

Also from trigonometry , for any angle B,

AC^2 = AB^2+BC^2 - 2AB*BC cosB....(1).

1 > CosB > 0 for B< 90 deg

CosB = 0 for B = 90 deg.

-1 < Cos B < 0 for B>0.

Therefore,

AC^2 < AB^2+BC^2 for B < 90.

AC^2 = AB^2+BC^2 for B = 9 deg.

AC^2 > AB^2+BC^2 for B > 90 deg.

Therefore, a triangle is **acute , right or obtuse **according as the **square on the greatest side** is **less than, or equal to, or greater **than the sum of the **squares on the other two les**ser **sides**.

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