# Directional Dilemma

Geometry Level 5

Rainy season has begun in the Philippines. In relation to that, rain in Zamboanga City falls in a specific direction such that

a.) when facing North, the rain falls $$60^{\circ}$$ from the horizontal towards East;
b.) when facing East, the rain falls $$30^{\circ}$$ from the horizontal towards North.

If it is solely a straight wind that causes the rain to fall in such direction constantly, neglecting all other forces (gravity, earth's rotation, etc.) then on top view, from what direction did the wind originate? Measure the exact angle relative to East to the nearest degree. Also assume that a counterclockwise rotation is positive.

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