A boat travels due north for 6 km, and then changes course and travels due west for 3 km.It changes course one more time to travel due south for another 2 km, where it drops anchor.What is the true bearing from where the boat starts to where it drops anchor?Leave your answer correct to the nearest degree.

To solve this problem, we need to use the Pythagorean theorem and trigonometry. Here are the steps:

1. First, we need to determine the total distance traveled in the north-south direction and the total distance traveled in the east-west direction. The boat travels 6 km north, then 2 km south, for a total of 4 km north. It also travels 3 km west.

2. Next, we draw a right triangle with the north-south distance as one leg and the east-west distance as the other leg. The hypotenuse of this triangle is the straight-line distance from the start to the end of the boat's journey.

3. We can use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we calculate √((4 km)^2 + (3 km)^2) = √(16 km^2 + 9 km^2) = √25 km^2 = 5 km.

4. Now, we need to find the angle of the true bearing. This is the angle between the north direction and the line from the start to the end of the boat's journey, measured clockwise. We can use the tangent function to find this angle. The tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle. So, we calculate tan^-1(3 km / 4 km) = 36.87 degrees.

5. Since the bearing is measured clockwise from north, the true bearing is 360 degrees - 36.87 degrees = 323.13 degrees.

6. Rounding to the nearest degree, the true bearing is 323 degrees.