Angular size in degrees problem,

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Homework Help Overview

The discussion revolves around calculating the angular size of distant objects, specifically the headlights of a car located 13 km away, with a width of 1.5 m. The original poster presents a formula for angular size in degrees and seeks assistance with their calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of the formula "57° (w/d)" and question whether it might be "0.57(w/d)". There is also a mention of using the cosine function for angular size calculations.

Discussion Status

Some participants provide guidance on the conversion between radians and degrees, suggesting that the original poster may have misunderstood the expected units in their calculations. There is a recognition of different interpretations of the formula and its application.

Contextual Notes

There is an indication that the original poster's calculations may have been in radians rather than degrees, which could have contributed to their confusion. The discussion reflects varying interpretations of the formula provided in the homework statement.

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Homework Statement



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?

Homework Equations



D/w

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!
 
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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
 
astru025 said:

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!

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).
 
Okay thanks I did 57 x (1.5/13000) and got .0066 degrees which was correct. Thanks
 

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