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?

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  • ?
    Lv 7
    4 weeks ago

    Google. There's quite a few solutions even on Y!A.

  • 4 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)

    Attachment image
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