干す and 乾かす: Spreading beans to dry and drying objects
Compare 干す for laundry or spread-out beans with 乾かす for shoes or paint. Read the mat-and-beans example without restricting 干す to hanging things.
Putting out or spreading things to dry
干す means to dry or hang out. 「晴れたので庭に洗濯物を干す。」 says it has cleared up, so the speaker is hanging laundry out to dry in the yard. It is a use involving putting laundry outside.
「収穫した豆をござの上に広げて干した。」 reports spreading harvested beans on a mat to dry. 広げて states that they were spread out, rather than suspended.
Drying objects with 乾かす
乾かす means to dry. 「洗った靴を日当たりのよい場所で乾かす。」 describes drying washed shoes in a sunny place. The shoes are the objects of the drying action.
「絵の具を乾かしてから次の色を塗った。」 reports letting paint dry before applying the next color. The actions have a stated sequence.
Method and overlapping scope
干す appears with both yard laundry and spread-out beans. 乾かす appears with shoes and paint and is not restricted to forced drying with a tool.
Because the actions can overlap, hanging versus using a machine is not a fixed division. Read the beans’ stated spreading and the next color following paint drying within their individual sentences.
How were the beans placed in 豆をござの上に広げて干した, and does 干した alone mean they were hung up?
Show the answer and why
They were spread on a mat to dry. This use of 干した is not limited to hanging things; 広げて states the actual placement.