Problem
Astronomers often measure large distances Using astronomical vosu (AU) vohere i) AU is the average distance from Earth to the Sun. In the image, drepresemts the distance from a star to the Sun. Using a technique called "stellar parallax" astronomers determined $\theta$ is 0.00001389 degrees. NOT TO SCALE a. How far away is the star from the Sun in astronomical units? Round your answer to the nearest thousand.
Solution
Step 1 ：Convert the angle θ from degrees to radians: \(\theta_{radians} = \theta_{degrees} \times \frac{\pi}{180}\)
Step 2 ：Use the formula for stellar parallax to find the distance in astronomical units: \(distance_{AU} = \frac{1}{\sin(\theta_{radians})}\)
Step 3 ：Round the distance to the nearest thousand: \(\boxed{4,125,000}\)
