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Angular size in degrees problem, please help!

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data

    For distant objects, the angular size in degrees can be approximated as 57° (w/d), where w is the width of the object and d is its distance. What is the angular size of the headlights on a car 13 km away if the headlights are 1.5 m apart?

    2. Relevant equations

    D/w

    3. The attempt at a solution
    13 km to m = 13000 m. 1.5 m / 13000 m = 1.15E-4. This answer was incorrect and I'm trying to figure out what I'm doing wrong. Any help would be really nice, thanks!
     
  2. jcsd
  3. Nov 23, 2013 #2

    CWatters

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    What does "57° (w/d)" mean?

    Are you sure it doesn't say "0.57(w/d)" ?

    I ask because the correct angle would be about Cos-1(w/d) which is 0.66 E-4 and..

    0.66/1.15 = 0.57
     
  4. Nov 23, 2013 #3
    The answer is not incorrect but it is in radians.
    Your problem "expects" you to calculate in degrees. Why don't you just apply the full formula given in the text? Multiply by 57 degree.
    The factor of 57 is the approximate conversion factor between degrees and radians. (57 degrees/radian).
     
  5. Nov 23, 2013 #4
    Okay thanks I did 57 x (1.5/13000) and got .0066 degrees which was correct. Thanks
     
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