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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
7, 8, 11
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.
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 lesser sides.
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