Caption: A right triangle illustrating the meaning of some common terms of trigonometry: adjacent, opposite, hypotenuse. The angles of the right triangle are A = 30°, B = 60°, and C = 90°.

Angle A is a parallax if it were measured by moving along the opposite (which is the baseline for the parallax) and measuring the shift in angular position of vertex A (which is just angle A itself) against the background of remote reference points.

We can calculate distance b using angle A and baseline distance "a" using trigonometry:

tan(A)=a/b , therefore b=a/tan(A) .If angle A is very small, we can make the small-angle approximation tan(A)≅A and obtain to 1st-order in small A

b=a/A ,where angle A is measured in radians.

Radians are the
natural units
for measuring angles---but they are
**NOT** always convenient units since there are an
irrational number of them
in a circle: i.e.,
2π = 6.283185307179586 ....
The conversion formula
from degrees
to radians is

θ(radians) = θ(°)*(2π radians/360°).Astro-bodies are usually so remote that their parallaxes are tiny for any baseline that we can use. Thus, the small-angle approximation virtually always gives negligible error.

Credit/Permission: User:TheOtherJesse,
2007 /
Public domain.

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