3470.12 – Radio Antenna

A wire for a radio antenna is to be strung from the roof of Aristides’s house to the roof of his friend’s garage. The garage is 40 feet from the house. The roof of the house is 45 feet high where the wire is to be fastened, and the roof of the garage is 15 feet high.

How long must the wire be?

Solution

Part (a) of the figure illustrates the situation. We extract there from the triangle in part (b). Now $30^2 + 40^2 = w^2$, so $w \geq 50$, because it will sag.

If Aristides sends his brand new, pet kitten across the wire to his friend in a bucket, it'll be a wild ride.