SOLUTION: Venus rotates in a nearly circular orbit around the sun. the largest angle form by Venus, Earth, and the sun is 46.5 degrees. The distance from the earth tot the sun is approximate

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Question 1014717: Venus rotates in a nearly circular orbit around the sun. the largest angle form by Venus, Earth, and the sun is 46.5 degrees. The distance from the earth tot the sun is approximately 149 million kilometers. What is the orbital radius of r of Venus? Round the nearest to the nearest million kilometers.
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
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Venus rotates in a nearly circular orbit around the sun. the largest angle form by Venus, Earth, and the sun is 46.5 degrees.
The distance from the earth tot the sun is approximately 149 million kilometers. What is the orbital radius of r of Venus?
Round the nearest to the nearest million kilometers.
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Make a sketch:

The Sun is at the origin of the coordinate system.

The Earth is on its circular orbits with the radius of 149%2A10%5E6 kilometers.
Put it as (represent it by) the point on the x-axis.

Venus is on its circular orbit which is located inside the Earth's orbit.

Draw the tangent line from the point representing Earth to the Venus circular orbit.

Draw the radius from the origin (where the Sun is located) to the tangent point at the Venus orbit.
As you understand, the radius is perpendicular to the tangent line. You should know it.

Did you complete this sketch?
If so, very good.

Now, the orbital radius of Venus is r = 149%2A10%5E6%2Asin%2846.5%5Eo%29 kilometers.

Please make all necessary calculations yourself.

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After submitiing my responce, I did the calculations myself (using the derived formula) and got that
the Venus orbital radius is about 107%2A10%5E6 kilometers.

Then I compared it with what Wikipedia says: 108%2A10%5E6 kilometers.

Not bad match!