Problem: The sides of a triangle are in the ratio . Then:
Answer Choices:
A. the triangle is obtuse
B. the angles are in the ratio
C. the triangle is acute
D. the angle opposite the largest side is double the angle opposite the smallest side
E. (none of these)
Solution:
Since , the triangle is acute, so that (C) is a correct choice. A check of (D) by the Law of Sines or the Law of Cosines shows that it is incorrect. (B) is obviously incorrect by the Law of Sines. Note: The elimination of (B) and (D) involves trigonometry, and so, in part, this problem is beyond the indicated scope.