Modeling Prompt

Ask students to think about a time when they went to a tall building or another place with a view, and invite students to share where they went and what the experience was like—for example, how far could they see? This distance defines their horizon.
 
Then ask students how they might represent a tall object on a sphere with pencil and paper, and what the segment between the top of the tall object and the horizon would look like. Here is an image to guide your planning:

One key part of the diagram is that right angles are formed where the tangents meet the radii at the points of tangency. Make sure to ask students to explain how they know these are right angles. Tell students that they will use diagrams like this to investigate different heights and horizons.