# The supergiant star Betelgeuse has a measured angular diameter of 0.044 arcsecond. Its distance has been measured to be 427 light-years. What is the actual diameter of Betelgeuse?

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This is a pretty straight forward trigonometry problem. We can set up a diagram showing that the distance to Betelgeuse and the radius of Betelgeuse make a right angle.

Therefore, we can use the

Since

But the radius is

Canceling the

Now we have an expression for the diameter, we can plug in what we know.

Light years are not the most practical units for measuring the diameter of a star, however, so lets convert to

This is about 600 times the diameter of the sun!

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It has a diameter of 861744026,4 km, so

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In astronomy, the angular diameter is given by the following formula:

206265 is simply the number of arcsecs in a radian.

So before we chuck in the values we have to rearrange the equation in a way that we isolate

Now to turn our

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