Final answer:
To find the distance from Atlanta to Augusta, we calculate the distances for each leg of the journey and then apply trigonometric methods to determine the direct distance between the two cities.
Step-by-step explanation:
The distance from Atlanta to Augusta, considering the given bearings and travel times, requires applying trigonometry to find the resultant vector of the two legs of the journey. From Atlanta to Macon, the car travels 75 miles (since it travels for 1 hour and 15 minutes at a speed of 60 mph). The bearing is S 27° E which implies a south-east direction. From Macon to Augusta, the second leg of the journey, the car covers 105 miles (traveling for 1 hour and 45 minutes at the same speed) on a bearing of N 63° E, heading northeast.
To calculate the distance from Atlanta to Augusta, we construct a triangle with the two given legs and calculate the hypotenuse. This problem can be solved using the law of cosines or by decomposing the legs into north-south and east-west components and then using the Pythagorean theorem to find the direct distance.