# When at closest approach to Earth, Planet X is observed to be 3.8 arcseconds in diameter. What is Planet X's diameter in meters?

There is no enough data. You need to know the distance to the planet.

One can obtain an expression by:

Converting arcsecs to radians

Imagine for a moment that the distance is 50 million kilometers (Mars or Venus may be that far away):

(Not Mars, nor Venus.) The diameter will be 920 thousand meters.

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To find Planet X's diameter in meters, we need to use the formula:

diameter (meters) = angular diameter (radians) × distance to planet (meters)

First, we convert the angular diameter from arcseconds to radians:

1 arcsecond = 4.848 × 10^-6 radians

Angular diameter in radians = 3.8 arcseconds × 4.848 × 10^-6 radians/arcsecond

Next, we need the distance to Planet X. Since this information is not provided, let's assume an average distance from Earth to Mars, which is about 225 million kilometers or 225,000,000,000 meters.

Diameter in meters = Angular diameter in radians × Distance to planet in meters

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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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