Question 1073781
 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(2.1345(10^-4)) = 9.3(10^7)/d}}}
{{{d = 9.3(10^7)/sin(2.1345(10^-4))}}}
Using the calc
d = 2.496(10^13) miles
Change to light years
{{{2.496(10^13)/5.879(10^12)}}} =  .425(10) = 4.25 light years