The proof in two minutes
From the USA and Canada, the Qiblah is toward the southeast. Here is why, in five points, all from the book.
We are ordered to face the direction.
Allah said in Suratul-Baqarah, verse 150:
وَمِنْ حَيْثُ خَرَجْتَ فَوَلِّ وَجْهَكَ شَطْرَ الْمَسْجِدِ الْحَرَامِ وَحَيْثُ مَا كُنتُمْ فَوَلُّواْ وُجُوهَكُمْ شَطْرَهُ
Ash-shatr means the direction. So one who is far from the Ka^bah has to seek its direction by the signs Allah has shown.
The direction is known from where a country lies from Makkah.
When the Companions placed a mihrab, they looked at where the country lay from Makkah. Abu Hanifah stated it: the Qiblah of the people of the west is toward the east, of the east toward the west, of the north toward the south, and of the south toward the north.
North America is north of Makkah.
The North Star stands higher above the horizon in the USA and Canada than it does in Makkah. So they lie north of it, and the one praying there turns to the south.
And it is west of Makkah.
So the one praying there also turns to the east. South and east together give the southeast. Al-Maqrizi wrote: for one “between north and west of the Ka^bah, the direction of his Qiblah is between south and east.”
The scholars have ruled on it.
The Chairman of the Fatwa Committee of al-Azhar wrote that “North America falls in the northwestern quarter with respect to Makkah.” The muftis and scholars in the book say the same, and Muslim graves from before 1937 in Sacramento and in Truro, Nova Scotia, face the southeast.
It is easy to check
No calculation is needed. The sunrise shows the east and the North Star the north. Islam does not oblige anyone to learn spherical trigonometry in order to pray.
From the book “The Qiblah in North America”: www.qiblah.us