How much of the drive will you pick up a signal from the transmitter?

Question

A small radio transmitter broadcasts in a 43 mile radius. If you drive along a straight line from a city 53 miles north of the transmitter to a second city 54 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer = ____ miles

Answer 1

43 mile radius

53 miles north of the transmitter

54 miles east of the transmitter

how many miles will you be in range of the transmitter?

plot the points on a graph. origin (0,0) is the transmitter's location

53 miles north is the point (0,53) 54 east is (54,0)

draw a straight line from the two last points

draw a quarter circle with the origin as the center, radius of 43

find where the line intersects the circle

circle is x^2 + y^2 = 43^2

the line is y -53 = (-53/54)(x-54)

y= -53x/54 +106

x^2 + (-53x/54 + 106)^2 = 43^2

but if you try to solve for x or y

you get only imaginary solutions

the circle never intersects the line

driving straight means never being within range of the transmitter

Answer: 0 miles

or if you want find the two imaginary solutions and find the distance between them, an imaginary distance, but that's not realistic