Problem:
A ship sails 10 miles in a straight line from A to B, turns through an angle between 45∘ and 60∘, and then sails another 20 miles to C. Let AC be measured in miles. Which of the following intervals contains AC2?
Answer Choices:
A. [400,500]
B. [500,600]
C. [600,700]
D. [700,800]
E. [800,900] Solution:
By the Law of Cosines,
AC2=AB2+BC2−2⋅AB⋅BC⋅cos∠ABC=500−400cos∠ABC
Because cos∠ABC is between cos120∘=−21 and cos135∘=−22, it follows that
