Distance between two cities

Mathematics
Tutor: None Selected Time limit: 1 Day

The bearing from Winston-Salem, North Carolina, to Danville, Virginia, is N 42 degrees E. The bearing from Danville to Goldsboro, North Carolina, is S 48 degrees E. A car is driven by Mark Ferrari, traveling at 60 mph, it takes 1 hr to go from Winston-Salem to Danville and 1.8 to go from Danville to Goldsboro. Find the distance from Winston-Salem to Goldsboro. 

Jun 14th, 2015

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The bearing from Winston-Salem to Danville is N 42° E.
The bearing from Danville to Goldsboro is S 48° E.
Mark, driving at 60mph, takes one hour to go from Winston-Salem to Danville
and 1.8 hour to go from Danville to Goldsboro.
Find the distance from Winston-Salem to Goldsboro.

diagram on based on the given data:

 N           D
    :           *
    :         * : *
    :   60  *42°:48°*
    :     *     :     *
    :42°*       :       *  108
    : *         :         *
  W *           :           *
    :       *   :             *
    :           :   *           *
    :           :           *     *
    :           S                   * G


"The bearing from Winston-Salem to Danville is N 42° E."
. . / NWD = 42° . . . hence: / WDS = 42°.


"The bearing from Danville to Goldsboro is S 48° E."
. . / SDG = 48°.


"Mark, driving at 60mph, takes one hour to go from Winston-Salem to Danville"
. . WD = 60

"and 1.8 hour to go from Danville to Goldsboro."
. . DG = 108


Note that: ./ D .= .42° + 48° .= .90°
. . ∆ WDG is a right triangle!


Use the Pythagorean Theorem to determine WG.

WG^2 = WD^2 + DG^2

WG^2 = 60^2 + 108^2

WG^2 = 3600 + 1164

WG^2 = 15264

WG = 123.54


the distance from Winston-Salem to Goldsboro is 123.54 mph

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 14th, 2015

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