i'd love some help

Question

A small radio transmitter broadcasts in a 46 mile radius. If you drive along a straight line from a city 64 miles north of the transmitter to a second city 60 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

46 mile radius

construct a line from (0, 64) to (60,0)

y =( -16/15)x + 64

then construct a circle

x^2 + y^2 = 46^2

calculate where the line and circle intersect

find those 2 points (if any) and calculate the distance between them.

x^2 + (-16x/15 +64)^2 = 46^2