The diameter of 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 from an angle of 2 degrees. how far away is this star from the earth?

The triangle formed is an isosceles triangle assuming that the orbit is circular. Get the measure of the third angle:
180 - 2(2) = 176°

Next, use the cosine law to solve for the distance of the star from the Earth
d = sqrt[ 186² + 186² - 2 x 186 x 186 cos 176° ]
d = 371.77

The distance of the start from Earth is 371.77 millions miles.