Medium

Pure Math

A $50-$ft ladder is placed against a vertical wall of a large building. The base of the ladder is in oil, which makes the base slip and the tip of the ladder slide down the wall. The base of the ladder slips away from the wall at a constant rate of $4$ feet per minute. Find the rate at which the angle between the ladder and ground is decreasing (in radians per minute) when the base of the ladder is $30$ feet away from the wall.

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