Nomadic tribe route

Geometry Level 3

A nomadic tribe in the northern hemisphere moves along the following route every year:

  • In spring, the tribe moves 100 km to the east.
  • In summer, the tribe moves 100 km to the north.
  • In autumn, the tribe moves 98 km to the west.
  • In winter, the tribe moves 100 km to the south.

The tribe reaches its exact starting point from the spring and sets up its winter quarters there.

At what latitude \(\phi\) are the winter quarters (in degrees)? Round to the nearest integer.

Note: Earth's radius is \(R = 6371 \,\text{km}.\)

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