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?
RealPro
Google. There's quite a few solutions even on Y!A.
billrussell42
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)