A piece of wire for a radio antenna is to be strung from the roof of Andrea’s house to the roof of the garage. The garage is 40 feet from the house. The roof of the house is 45 feet high at the edge where the wire is fastened, and the roof of the garage is 15 feet high. The wire must be at least how long?

We see this:

30

so

^{2}+ 40^{2}=*w*^{2},so

*w*≥ 50 (because it will sag).