W A Trigonometry is used to measure the distance to stars in the solar system, and the motion of'nearb'y stars compared to more distant stars. The method of measuring distance in space is called trigonometric parallax. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, the star is observed at two different times exactly two months apart, and its apparent change in position is recorded. From these two observations LEISEz can be calculated. (The times are chosen so that (.E'ISE2 is as large as possible, which guarantees that AEIOS is 90}. The angle 419105 is called the parallax of the star; Alpha Centauri, the star nearest the earth, has a parallax of 0. 000211" . Estimate the distance to this star. [Take the distance from the earth to the sun to be 9. 3X10? mi.)