A small radio transmitter broadcasts in a 54 mile radius. If you drive along a straight line from a city 71 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?

Guest Apr 17, 2023

#1**0 **

x^2 + y^2 = 54^2 is a circle with radius 54

y= -71/66*x + 71 is the line of travel

find where the line intersects the circle

then find the distance between those 2 intersection points

the points are (53.4, 8.03) and (18.22, 50.83)

distance between them = about 62.23 miles within the radio transmitter

Guest Apr 17, 2023