4. Solve the triangle(s), if possible. Round to the nearest tenth.

Question

Solve the triangle. Side a = 8, side b = 10, side c = 12

6. Two boats leave the same dock at the same time. The first sails in a straight line
N40°W at 36 miles per hour and the second goes in a straight line S12°W at 62 miles per hour.
After 1 hour, how far apart are the boats, to the nearest tenth of a mile?

Answer 1

use the law of cosines for two of the angles, then the 3rd angle is trivial. For angle A,

10^2 + 12^2 - 2*10*12cosA = 8^2
similarly for B or C

For the boats, draw a diagram. Using the law of cosines, the distance d is found by

d^2 = 36^2 + 62^2 - 2*36*62 cos128°