SOLUTION: Tell if the measures 8, 9, and 8 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse.

Question 394551: Tell if the measures 8, 9, and 8 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Three real numbers form a triangle if and only if the sum of the shortest two sides is longer than the length of the third side.

Also, a triangle is acute when the sum of the squares of the two shortest sides is greater than the square of the third side (this comes from the Law of Cosines).

Since 8 + 8 > 9, the sides make a triangle. Also, since 8^2 + 8^2 > 9^2, the triangle is acute.

(You may have learned the triangle inequality that says that the sum of any two lengths must be greater than the third length. This is true, but the easiest way to check three lengths is to sum the shortest two. For example, if a, b, c are the side lengths such that we already know that b+c > a, a+c > b since c > a, c > b, so it only remains to show that a+b > c. Same analogy applies to the acute/obtuse/right identity.)
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