Question

A small radio transmitter broadcasts in a 53 mile radius. If you

drive along a straight line from a city 73 miles north of the
transmitter to a second city 66 miles east of the transmitter,
during how much of the drive will you pick up a signal from the
transmitter?

________ miles

Answer 1

29% of the drive

The distance that you get reception is the length of the chord created by the intersection of the circle defining the edge of transmission and the line defining the car trip.

x2 + y2 = 532 this is the circle

y = -70x/73 + 70 this is the line

1. solve by substitution

2. determine the distance between two solutions (the intersections)

3. this is the distance during which the radio is heard.