Bridge Over...Semicircle

Geometry Level 1

There is a semi-circular object on a road and a strong metal plate is put on it, as shown in the above diagram, so that cars can better pass over it. If the radius of the object is \(28\) inches and the angle between the plate and the road is \(30^\circ,\) what is the distance (in inches) between the point the plate meets the road and the point the plate touches the semi-circular object?

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