# Precalc question ?

A small radio transmitter broadcasts in a 56 mile radius. If you drive along a straight line from a city 72 miles north of the transmitter to a second city 62 miles east of the transmitter, much of the drive will you pick up a signal from the transmitter?

### 2 Answers

- billrussell42Lv 74 weeks ago
see drawing. You want the length of AB

eq of circle is x²+y² = 56²

equation of line:

Two points form of line eq.

y – y₁ = (x – x₁)(y₂ – y₁) / (x₂ – x₁)

y – 72 = (x – 0)(0 – 72) / (62 – 0)

y – 72 = (– 72x) / (62)

y = –(72/62)x + 72

points A and B are solutions to the two equations

x²+y² = 56²

y = –(72/62)x + 72

once you get the solutions, which define A and B, then the length of the line AB you can get from...

distance between two points

d = √(Δx² + Δy²)

which is the answer if you want miles.

if you want percentage, divide that by the length of CD which is

√(72² + 62²)