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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