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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?

 Apr 17, 2023
 #1
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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

 Apr 17, 2023
 #2
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Thank you!

Guest Apr 18, 2023

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