1. The ship is our starting point.
2. The whirlpool is 40 km due north. That's like due "up" on our map.
3. The volcano is east of the whirlpool, but we're given its bearing from the ship, which is 058°.
A bearing of 058° means the volcano is northeast of the ship, but more towards the north than the east.
Now, Archie wants to sail through the midpoint between the whirlpool and the volcano. We'll assume the whirlpool and volcano are directly east-west of each other (since we lack the east-west distance).
Here's the plan:
1. Draw a right triangle where the ship and the whirlpool form one leg (north), and the ship and volcano form the hypotenuse.
2. The angle at the ship is 58° (from the bearing).
3. We need to find the angle of Archie's path with respect to north. This path will bisect the angle formed by the line to the whirlpool and the line to the volcano.
Let's calculate this angle.
Archie should set sail on a bearing of 29° to pass through the midpoint between the whirlpool and the volcano. Sounds like a daring adventure, doesn't it? Just watch out for any sea monsters lurking around!