Direction and determining the Qiblah

QIt is very clear in suratu al-Baqara that the qiblah is for one to face al-masjid al-haram wherever one is. However, I am noticing that people are relying on calculations and mathematical formulas to figure out the qiblah. In your opinion is that acceptable? What if one is living in a remote area and have no access to computer how would that person determine the Qiblah?

Also, why here in North America we face northeast when praying. I feel that if I keep walking in the direction of northeast I would hit the Scandinavian countries and not Mecca in Saudi Arabia.

A Your question will be answered if you differentiate between the actions and the tools. For example, journey (traveling) is action, but camel, car, donkey, airplane, horse or bike are tools or means; fighting is action, but sword, gun, spear, grenade, arrows and missiles are tools or means. The rule is that unless a tools or mean has been clearly prohibited, we can use the available means to perform Islamic actions. We can go to Hajj by air, we do not have to insist on going on camel. We need to stop eating at dawn, whether we determine dawn by looking outside in a jungle or we use the calculations and compass in a major city. In the same manner, we need to determine the direction of Qibla for our Salaah, whether we look at stars to determine it, or we calculate its angle and use compass to determine it.

As for the direction in North America, if you look at a flat map, yes you are right, northeast seems to take us to the wrong side. But remember that earth is not flat, it is a globe. So if you walk at the precise calculated degree angle in the north east direction from North America on the globe, you will definitely end up in Makkah. And that will be the shortest distance from here to there.

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