How to correctly calculate the direction to travel farther away?
To determine directions for overseas locations, a typical "world map" cannot be used to measure directions.
When determining directions for overseas locations, conventional world maps are not used. Using such maps could lead to significant inaccuracies.
Instead, specialized maps are employed for determining directions overseas, such as globes or cartographic projections like Lambert azimuthal equal-area projection (as shown below) or equidistant azimuthal projection (Houi-Tori maps).
This projection method creates maps where the land's area and shapes may differ from reality, but the directions are accurately represented. It's a map designed specifically for Houi-Tori. Commercially available versions of these maps depict Japan at the center. Obtain one of these maps and try drawing directional lines on it.
Points to note
The smaller the scale of the map, the larger the errors become. Even with a 1/220 million scale map of Japan, significant considerations for errors are necessary. Significant scaled-down maps (1/many million) are used when determining directions for overseas locations. The variations in maps and errors in directions for overseas locations are far more substantial than those within the country.
Bonus
When looking from Japan, Hawaii is in the eastern direction.
Here's a question: If you were in Hawaii looking towards Japan, which direction would it be?
The answer is northwest!
If we consider short distances, it would be the opposite direction: west. However, the Earth is round, leading to these intriguing situations. For trips abroad lasting less than two months, you only need to consider the direction you're going. But if your stay abroad is over two months, you'll need to think about the direction for your return. In that case, please be sure to consult with professionals.