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For best illumination of a piece of art, a lighting specialist for an art gallery recommends that a...........


celing-mounted light must be 6 feet from a piece of art and that the angle of depression of the light must be 38 degrees. HOW FAR FROM A WALL should the light be placed so that the recommendations of the specialist are met? Notice that the art extends outward 4 inches from the wall.

The hypotenuse of the triangle would be 6 feet and the angle would be 38 degrees. You want to find out the length of the adjacent side. That calls for cosine.

cos 38 degrees = adjacent / 6 or
adjacent = 6 * cos 38 degrees = about 4.7280645216403317401638667270151 feet = about 4 feet 8.7367742596839808819664007241813 inches.

Then you have to account for the 4 inch extension of the art, so the light would want to be about 5 feet 0.7367742596839808819664007241813 inches away from the wall.

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