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Tell whether the measures can be the side lengths of a triangle. If so, classify the...

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recyclegogreen | Student, Grade 11 | (Level 1) Honors

Posted November 29, 2010 at 6:24 AM via web

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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.

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pops2 | Student, Undergraduate | (Level 1) Honors

Posted November 29, 2010 at 6:27 AM (Answer #1)

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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)

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neela | High School Teacher | (Level 3) Valedictorian

Posted November 29, 2010 at 2:39 PM (Answer #2)

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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 lesser sides.

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