Using binoculars, a bird-watcher spots an osprey nest on top of a light pole $50\text{ feet}$ tall. He then walks a constant rate of $4\text{ miles per hour}$, for $3\text{ minutes}$ on level ground to reach the base of the light pole. The height of the bird-watcher is $5\text{ feet}$.

What was the angle of elevation to the nest when he first spotted it, to the nearest hundredth of a degree?

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