For two hours, a boat sails straight from port A to port C with a speed of 50 miles per hour. Port B is due east of port A, and the bearing of line segment BC is 20 degrees south west. Find the bearing of line segment AC. I really don't know what's the first thing to do.
I interpret your language to mean that BC is 20° south of west.
I assume that the two-hour cruise from A actually arrived at port C, meaning AC is 100 mi.
In problems like this, the first thing to do is always to draw a diagram. If you cannot do that, you have no hope of solving the problem.
So. Now you have a triangle with the angle between AB and BC is 20°, and AC = 100.
There is something missing here. All we have is one angle and the side opposite it. That gives us no way to figure the other angles. Do we know how far B is from A or C?
To find the bearing of line segment AC, we need to break down the problem into steps. Here's how you can approach it:
Step 1: Draw a diagram:
Draw a triangle to represent ports A, B, and C. Label port A as the starting point and port C as the destination.
Include a line segment BC, which is due east from port A.
Step 2: Determine the angle of line segment BC:
The problem states that the bearing of line segment BC is 20 degrees southwest. Since it is southwest, it means it is between south and west, so it makes an angle of 20 degrees with the south direction.
Step 3: Calculate the angle of line segment AC:
To find the bearing of line segment AC, we need to determine the angle from the north direction to line segment AC.
Since the boat sailed straight from port A to port C, line segment AC will be a straight line. Therefore, we can draw a straight line from port A to the north direction.
Step 4: Find the supplement angle:
The supplement angle is the angle that, when added to the angle between the north direction and line segment AC, gives a total of 180 degrees.
In this case, the supplement angle is the angle between the north and the line segment BC, which is 20 degrees (from Step 2).
Step 5: Determine the bearing of line segment AC:
To find the bearing of line segment AC, subtract the supplement angle from 180 degrees. This will give you the angle between the north direction and line segment AC.
Step 6: Calculate the final bearing:
The final bearing is the angle measured clockwise from the north direction to line segment AC.
Follow these steps to find the bearing of line segment AC.