The lengths of the sides of a triangle are 6, 5 and 7. Classify the triangle as acute, right, or obtuse.

Answer 1

Let a=5, b=6 and c=7,

Then to be a right triangle, c^2 must exactly equal a^2+b^2,

To be an obtuse triangle, c^2 must be greater than a^2+b^2

Finally, to be an acute triangle, c^2 must be less than a^2+b^2

For this particular example, a^2=25, b^2=36, and c^2=49

Clearly, a^2+b^2=61, which makes c^2 less than this total. Therefore, this particular triangle is ACUTE (containing 3 angles, each of which measures less than 90 degrees) and is also SCALENE by virtue of having 3 unequal side lengths.

Answer 2

Applying the law of cosines, the angles are:

78.46

44.42

57.12

It is an acute triangle