A small radio transmitter broadcasts in a 29 mile radius. If you drive along a straight line from a city 32 miles north of the transmitter to a second city 40 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter

He will pick up a signal from the transmitter 29.43 miles of the drive.

Step-by-step explanation:

Since we have given that

Radius = 29 mile

So, equation of circle would be

There is a straight line from a city 32 miles north i.e. (0,32) to a second city 40 miles east of the transmitter i.e. (40,0)

So, equation of line would be

So, we will put this value in the equation of circle.

So, x= 4.12 and x = 27.1

So, y = 28.7, y = 10.32

So, distance between them would be

Hence, he will pick up a signal from the transmitter 29.43 miles of the drive.