10.1 Applications of Area and Law of Cosines

For each problem, on a separate sheet of paper,

a) Draw a sketch

b) Write and equation and show any necessary work

c) Round answers to the nearest tenth.

  1. A ranger in an observation tower can sight the north end of a lake 15 km away and the south end of the same lake 19 km away. The angle between these two lines of sight is. How long is the lake?
  1. A triangular-shaped lot of land has sides of length 130m, 150m and 80m. What are the measures of the angles?
  1. Two streets meet at an angle of. If a triangular lot has frontages of 60m and 65m on the two streets, what is the perimeter of the lot?
  1. An oil tanker and a cruise ship leave port at the same time and travel straight-line courses at 10mi/h. and 25mi/h respectively. Two hours later they are 40 mi apart. What is the angle between their courses?
  1. A large park in the shape of a parallelogram has diagonal paths that meet at a angle. If the diagonal paths are 12 km and 20 km long, find the perimeter of the park
  1. A vertical pole 20 m tall standing on a slope is braced by two cables extending from the top of the pole to two points on the ground, 30 m up the slope and 30 m down the slope. How long are the cables?
  1. The measure of two sides of a parallelogram is 50 cm and 80 cm, and one diagonal is 90 cm long. How long is the other diagonal?
  1. A triangular lot has two sides of lengths 90 meters and 52 meters and an included angle of 102. Find the length of the third side.0

9. A motorized sailboat leaves Naples, Florida bound for Key West, 150 miles away. Maintaining

a constant speed of 15 miles per hour, but encountering heavy crosswinds and strong

currents, the crew finds, after four hours, that the sailboat is off course by 20°.

a) How far is the sailboat from Key West at this time?

b) Through what angle should the sailboat turn to correct its course?

c) How much time has been added to the trip because of this? (Assume that the speed

remains at 15 miles per hour.)

10. A cruise ship maintains an average speed of 15 knots going from San Juan, Puerto Rico to

Barbados, West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the

captain heads out of San Juan in a direction of 20°off a direct heading to Barbados. The

captain maintains a 15 knot speed for 10 hours, after which time the path to Barbados

becomes clear of storms. Through what angle should the captain turn to head directly to

Barbados?