Angular size in degrees problem,

[astru025]

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!

 

[CWatters]

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

 

[nasu]

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).

 

[astru025]

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