posted by Michael on .
Suppose a triangle has side lengths of 6, 7, and 10. What best describes it? Acute, right, obtuse, or not enough information?
It is a scalene triangle. One angle is obtuse, and no two are equal.
The angle opposite the longest side is C. According to the Law of Cosines,
c^2 = a^2 + b^2 -2ab cos C.
Since c^2 is greater than a^2 + b^2, cos C is negative, so C is obtuse ( >90 degrees)