Astronomers use angles of elevation to find and measure stars and planets in the sky. This method is based on some basic math, especially right triangles.

Key Ideas:

1. What is an Angle of Elevation?:

   • An angle of elevation is the angle you make when you look up from a flat surface (like the ground) to see an object above you.
   • For example, if you look up at a star and measure an angle of 30 degrees, you can use that angle to figure things out.

2. Using Simple Math:

   • Astronomers use something called the tangent function, which is a way to relate different sides of a right triangle.
   • Think of it like this: $\tan(\theta) = \frac{\text{Height}}{\text{Distance}}$. Here, "Height" is how high the star is, and "Distance" is how far you are from the spot directly below the star.
   • If a star is 1,200 kilometers up and you measure the angle of elevation to be 30 degrees, you can find out how far away the star is by using this formula: $\text{Distance} = \frac{\text{Height}}{\tan(30^\circ)} \approx \frac{1200}{0.577} \approx 2076 \text{ km}$

3. Why This Matters in Astronomy:

   • This method helps astronomers find where objects are, measure distances within our solar system, and even estimate how far away distant galaxies are.
   • The angles of elevation provide important information for studying the universe.