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Angular Measure 2

Skinny Triangle Simplification

There is one important way we can speed up our calculations using angular measure. It's an interesting trick all astronomers are familiar with. It applies when the angle of the object we are observing is very small (much less than 1 degree). This is always the case when dealing with celestial objects.
Skinny triangles have a side length which is almost the same as their heights. Compare this to wider triangles that have much longer sides as compared to the heights. Now here is the trick. If we are dealing with skinny triangles we can assume they are right triangles and use trigonometry to solve for distance. Let's review.

New shortcut

If some object has a very tiny angular size, θ, then
tan(θ)θ=dD  (radians)
where, d = diameter and D = distance.
1 radian = 57.3 degrees = 57.3×3600=206265 arc seconds
This gives us the equation that we see most often:


Let’s try it out in the next exercise!

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