SOLUTION: A triangle has side lengths of 8 cm, 11 cm, and square root of 193 cm classify the angle. A. Obtuse B. Acute C. Right D. None of these

Algebra ->  Triangles -> SOLUTION: A triangle has side lengths of 8 cm, 11 cm, and square root of 193 cm classify the angle. A. Obtuse B. Acute C. Right D. None of these      Log On


   

Question 478257: A triangle has side lengths of 8 cm, 11 cm, and square root of 193 cm classify the angle.
A. Obtuse
B. Acute
C. Right
D. None of these
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a=8+cm, b=11cm, and c=sqrt%28193cm%29

c%5E2=a%5E2%2Bb%5E2
%28sqrt%28193%29%29%5E2=%288cm%29%5E2%2B%2811cm%29%5E2

193=64%2B121

193=185....since left side is not equal to right side, the triangle is NOT right triangle

an acute triangle satisfies a%5E2%2Bb%5E2%3Ec%5E2, b%5E2%2Bc%5E2%3Ea%5E2, and c%5E2%2Ba%5E2%3Eb%5E2.
since a%5E2%2Bb%5E2%3Ec%5E2 or 185 is NOT greater than 193, your triangle is NOT acute

For an angle to be obtuse,with C the angle opposite side C, cosC<0. Therefore, an obtuse triangle satisfies one of a%5E2%2Bb%5E2%3Cc%5E2, b%5E2%2Bc%5E2%3Ca%5E2, or c%5E2%2Ba%5E2%3Cb%5E2
in your case a%5E2%2Bb%5E2%3Cc%5E2 or 185%3C193; so, your triangle IS obtuse.