8 Applications of Trig

Standard 4.7 I can use the Law of Sines or Law of Cosines to solve real world scenarios

Example 1: Juan and Romella are standing at the seashore 10 miles apart. The coastline is a straight line between them. Both can see the same ship in the water. The angle between the coastline and the line between the ship and Juan is 35 degrees. The angle between the coastline and the line between the ship and Romella is 45 degrees. How far is the ship from Juan?

Example 2: Airplane A is flying directly toward the airport which is 20 miles away. The pilot notices airplane B 45 degrees to her right. Airplane B is also flying directly toward the airport. The pilot of airplane B calculates that airplane A is 50 degrees to his left. Based on that information, how far is airplane B from the airport?

Example 3: You are on a hill and can see two buildings in the distance. Suppose the buildings are six miles apart. If you are 3.2 miles from one building the angle between the two lines of sight to the buildings is 30.5 degrees, how far are you from the second building?

Example 4: To estimate the length of a lake, Caleb starts at one end of the lake and walks 95m. He then turns and walks on a new path, which is 120° to the direction he was first walking in, and walks 87m more until he arrives at the other end of the lake. Approximately how long is the lake?

Example 5: Jack and Jill both start at point A. They each walk in a straight line at an angle of 105° to each other. After 45 minutes Jack has walked 4.5km and Jill has walked 6km. How far apart are they?

Example 6: Tom, Dick, and Harry are camping in their tents. If the distance between Tom and Dick is 153 feet, the distance between Tom and Harry is 201 feet, and the distance between Dick and Harry is 175 feet, what is the angle between Dick, Harry, and Tom?

Example 7: A triangular playground has sides of lengths 475 feet, 595 feet, and 401 feet. What are the measures of the angles between the sides, to the nearest tenth of a degree?

Example 8: : 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 46ft side.