a ship leaves port with a bearing of S 42deg W after traveling 7 miles, the ship turns 90deg and travels on a bearing of N 52deg W for 10 miles at that time, what is the bearing of the ship to the port?
N 36 degrees E
jdsh
To find the bearing of the ship to the port, we can break down the problem into two steps:
Step 1: Determine the new position of the ship after it turns 90 degrees and travels 10 miles.
Step 2: Find the bearing of the new position of the ship relative to the port.
Step 1: Determine the new position of the ship after it turns 90 degrees and travels 10 miles.
Let's consider the initial bearing of the ship as S 42° W. To find the new position, we need to consider the given information that the ship turns 90 degrees and travels 10 miles on a bearing of N 52° W.
First, we can convert the initial bearing of S 42° W into a bearing in terms of degrees from the north. Since the south direction is directly opposite the north direction, we subtract 42 degrees from 180 degrees (which represents a bearing due south) to get the bearing in terms of degrees from the north: 180° - 42° = 138° (measured clockwise).
Next, we know that the ship turns 90 degrees, so we add 90° to the current bearing of 138°: 138° + 90° = 228°.
Now, the ship is traveling on a bearing of N 52° W. We can convert this bearing into a bearing in terms of degrees from the north by subtracting 52 degrees from 180 degrees: 180° - 52° = 128° (measured clockwise).
To find the new bearing after the ship turns 90 degrees and travels on a bearing of N 52° W, we add the two bearings: 228° + 128° = 356°.
So, the new position of the ship is on a bearing of 356° from the port.
Step 2: Find the bearing of the new position of the ship relative to the port.
To find the bearing of the ship to the port, we subtract the new position bearing (356°) from 180 degrees: 180° - 356° = -176°.
However, it is more common to express bearing in terms of degrees clockwise from the north, so we need to adjust the bearing to be a positive value. We add 360 degrees to the negative bearing to obtain the positive bearing: -176° + 360° = 184°.
Therefore, the bearing of the ship to the port is N 184° W.