Pre-Calculus Honors

Law of Sines and Cosines

Sections 6.1 & 6.2

1. Points A an B are on opposite sides of the Grand Canyon. Point C is 200 yards from A. Angle B measures 87o and angle C measures 67o. What is the distance between A and B? 2. Two observers are standing on shore ½ mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. Angle A is 63o and angle B is 56o. Find the distance from each observer to the sailboat. 3. A person at point A looks due east and sees a UFO with an angle of elevation of 40o. At the same instant, another person, 1.0 miles due west of point A looks due east and sights the same UFO with an angle of elevation of 25o. Find the distance between A and the UFO. How far is the UFO above the ground? 4. A vertical flagpole is attached to the top edge of a building. A man stands 400 feet from the base of the building. From his viewpoint, the angle of elevation to the bottom of the flagpole is 60o; to the top is 62.5o. Determine the height of the flagpole. 5. Two sides and the included angle of a parallelogram have measures 3.2, 4.8, and 54o respectively. Find the lengths of the diagonals. 6. A bridge is supported by triangular braces. If the sides of each brace have lengths 63 feet, 46 feet and 40 feet, find the measure of the angle opposite the 46 ft side. 7. The measures of two sides of a parallelogram are 28 in and 42 in. If the longer diagonal has measure 58 in, find the measures of the angles at the vertices. 8. On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from Orlando, and Denver is 235 mm from Niagara Falls. Find the bearing of Denver from Orlando. Find the bearing of Denver from Niagara Falls. 9. Nancy shines a light from a window of a light house on a cliff 250 feet above the water level. Nick Danger 10 feet above the water level in a ship off shore, finds that the angle of elevation of the light is 3o. Find the length of the line of sight (light beam) from the ship to Nancy. Round to the nearest tenth. 10. Yogi bear is out walking with Boo Boo looking for a pic-i-nic basket and Boo Boo sights a bee hive up in a tree at an angle of elevation of 36o. They walk 120 meters closer to get a better look and then look up at an angle of elevation of 51o How far are Yogi and Boo Boo from the bottom of the tree from their current spot? 11. Two ranger stations are on an east-west line 110 miles apart. A forest fire is located on a bearing of N42E from the western station at A and a bearing of N15E from the eastern station at B. How far is the fire from the western station? 12. Flights 104 and 217 are both approaching O’Hare International Airport from directions directly opposite one another and at an altitude of 2.5 miles. The pilot on flight 104 reports and angle of depression of 1747’ to the tower, and the pilot on flight 217 reports an angle of depression of 1239’ to the tower. Calculate the distance between the planes. 13. You are taking a flight from Daytona Beach to St. Louis. There is a stopover in Atlanta. The bearing from Daytona Beach to Atlanta is N 38.3° W. The bearing from Daytona straight to St. Louis is N 43.4° W. The distance of the first leg of the trip from Daytona to Atlanta is approximately 599.8 kilometers. From Atlanta to St. Louis is another 748.4 kilometers. How long is the total trip including lay over? How much shorter would the trip be if the flight went directly from Daytona Beach to St. Louis? 14. An airplane is sighted at the same time by two ground observers who are 4 miles apart and both directly west of the airplane. They report the angles of elevation as 11 and 22. How high is the airplane?