# 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?

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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[ \text{Actual Diameter} = \text{Angular Diameter} \times \text{Distance} \times \frac{\pi}{180 \times 3600} ] [ \text{Actual Diameter} = 0.044 , \text{arcseconds} \times 427 , \text{light-years} \times \frac{\pi}{180 \times 3600} ] [ \text{Actual Diameter} \approx 1.09 , \text{million kilometers} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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