A small radio transmitter broadcasts in a 67 mile radius. If you drive along a straight line from a city 78 miles north of the transmitter to a second city 87 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Circle equation about the origin x^2 + y^2 = 67^2
Line equation between the two points y = 78/87 x -78 <===== insert this value of y into the circle equation to find the x values where the line crosses the circle.
Use these x values in the line equation (easiest) to calculate the y values
Use distance formula to calculate the distance between the points ......YOU can do the work
I find an answer AROUND 66 miles
what do you find?
You can also use graphical methods to find the intersection points (very easy) ....then distance formula between the points of intersection...