A small radio transmitter broadcasts in a 24 mile radius. If you drive along a straight line from a city 28 miles north of the transmitter to a second city 30 miles east of the transmitter

Question

A small radio transmitter broadcasts in a 24 mile radius. If you drive along a straight line from a city 28 miles north of the transmitter to a second city 30 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

graph the circle and line

find the intersection points

calculate the distance between them

(about 22.09, 9.38) and (7.84, 22.68)

are d apart

d= sqr(14.25^2 + 13.3^2) = about 19.49 miles