A small radio transmitter broadcasts in a 47 mile radius. If you drive along a straight line from a city 65 miles north of the transmitter to a second city 59 m

Question

A small radio transmitter broadcasts in a 47 mile radius. If you drive along a straight line from a city 65 miles north of the transmitter to a second city 59 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

 

 Transmitter at origin

 

 City to the north at (0,65)

 City to the east at (59,0)

 

 Slope is M=(-65/59)

 

 INtercept is B= y - mx =  65 - (-65/59)(0) = 65

 

The equation of the line between the cities is y = (-65/59)x + 65

 

 

x^2 + ( (-65/50)x + 65) )^2 = 47^2

 

Solving this quadratic and plugging into the line equation, the

intersection points are:

 

(20.698, 42.197) and (43.998,16.527)

The transmitter is within range between those to points along the line.

 

you can see the graph at desmos.com