Radio Transmitter

Question

A small radio transmitter broadcasts in a 58 mile radius. If you drive along a straight line from a city 81 miles north of the transmitter to a second city 71 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

find where x^2 +y^2 = 58^2

intersects the line y=-81x/71 + 71

there are 2 intersection points

calculate the distance between them, use the distance formula a version of the Pythagorean theorem

x^2+ (-81x/71 +71)^2 = 58^2

x^2 + (81^2)x^2 +71^2)/71 = 58^2, solve for x

or use a graphing calculator to find the two intersection points = about

(55.08, 18.16) and (25.28, 52.23)

calculate distance between those 2 points

d^2 = (55.08-25.28)^2 + (52.23-18.16)^2 = 29.80^2 + 34.02^2

d= about 45.23 miles in transmitter distance