SOLUTION: The diameter of the earth’s orbit around the sun is approximately 186 million miles. Looking at a star from the two points on the orbit which are furthest apart, the lines of sigh

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Question 1073781: The diameter of the earth’s orbit around the sun is approximately 186 million miles.
Looking at a star from the two points on the orbit which are furthest apart, the lines of sight
to the star form an angle of 4.269 × 10−4 degrees. How many light-years away is this star
from the earth? Note that one light-year is approximately 5.879 × 1012 miles.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The diameter of the earth’s orbit around the sun is approximately 186 million miles. 1.86(10^8)
Looking at a star from the two points on the orbit which are furthest apart, the lines of sight to the star form an angle of 4.269 × 10^-4 degrees.
How many light-years away is this star from the earth?
Note that one light-year is approximately 5.879 × 10^12 miles.
:
let d = distance from the earth to the star
Utilize a right triangle formed from the center of the orbit to a point on the orbit to the star.
Use half the given angle: 2.1345(10^-4) degrees
Use half the diameter of the orbit as the side opposite, 9.3(10^7) miles
Use the sine of the angle to find d (hypotenuse}
sin%282.1345%2810%5E-4%29%29+=+9.3%2810%5E7%29%2Fd
d+=+9.3%2810%5E7%29%2Fsin%282.1345%2810%5E-4%29%29
Using the calc
d = 2.496(10^13) miles
Change to light years
2.496%2810%5E13%29%2F5.879%2810%5E12%29 = .425(10) = 4.25 light years