A small radio transmitter broadcasts in a 49 mile radius. If you drive along a straight line from a city 54 miles north of the transmitter to a second city 67 miles east of the transmitter

Question

(the rest of the question) during how much of the drive will you pick up a signal from the transmitter?

Answer 1

about 46.9 miles

a circle's equation is: x^2 +y^2 = 49

the line's equation is y=-54x/67 +54

solve for x and y, 2 equations 2 unknowns

that gives you two points where the circle intersects the line

then find the distance between them

or construct a right triangle with vertices (0,0), (33.5, 27) and (x,y) (33.5,27) is the midpoint of the line segment from (0,54) and (67,0). hypotenuse of the right riangle is 49. one side is 43.026, the other side is half the distance between the two points where the circle intersects the line = sqr(49^2 -43.026^2)=about 23.45

find the distance between (33.5,27) and (x,y),= 23.45, multiply it by 2 to get about 46.9

it helps to draw a graph, if only to check your answer