Due to the symmetry of the triangle SAB we may calculate the distance from the Sun to the star as the height of the triangle.
Let AB=2a,∠ASB=2θ. So a=1.5⋅108km,θ=1′′.
The height d of an isosceles triangle is d=tanθa=tan1′′1.5⋅108km.
For small angles their tangents are approximately equal to the angle expressed in radians.
1′′≈2062651rad⇒d≈1.5⋅108km⋅206265≈3.1⋅1013km.
The speed of light is c≈3⋅105km/s, and there are 86400⋅365.24≈3.16⋅107 seconds in a year, so the light-year is 3.16⋅107s⋅3⋅105km/s=9.5⋅1012km.
Therefore, 1 pc is equal to 9.5⋅10123.1⋅1013≈3.3 light years.
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