Something which is 100 km away has an angular size of 2 seconds of arc.?

Question

I already know the answer is approx 1m. What I really need is guidance on how to get there. I know that a second of arc is 1/3600 of a degree. I worked the equation using that (1/180 based on 2 seconds of arc) and the tangent function, but that was incorrect.

Any help and direction is appreciated.

Answer 1

Use arc length = r x angle(radians)
There are 2 pi radians in circle =360 degrees= 60x360 min =60X60X360 sec =1296000 sec This give 1sec = 4.8x10^(-6) radians so 100000x2x4.8x10^(-6) =.96 meters

Answer 2

permit r be the radius of the Moon, d be the area of the Moon, and allow Alpha be a million/2 of the Moon's angular length. Then tan(Alpha) = r/d permit Beta be a million/2 of the Moon's angular length while it particularly is 7.12 situations farther away. Then tan(Beta) = r/7.12d = tan(Alpha)/7.12 because Alpha and Beta are small angles, we can replace the tangents with the angles themselves, so Beta is approximately equivalent to Alpha/7.12. Alpha is 15', so Beta is two.107'. on the grounds that's a million/2 the angular diameter, the in simple terms suitable answer is 4.2135 arc minutes. P. S. I did the calculation applying the tangents and have been given 4.214 arc minutes, so the version is rather easy.