Page 195 - IM_FL_Geometry_Print Sample

One key part of the diagram is that right angles that are formed where the tangents meet the radii at the points of tangency. Make sure to ask students to explain how they know these angles are right.
Student Task Statement
People like living at the top of tall buildings or hiking to the top of tall mountains because the views are amazing. From those heights, it is possible to see for great distances before the earth curves away from view at the horizon. For these problems, assume Earth is perfectly spherical with a radius of 6,371,000 meters and that there are no obstacles to the view.
1. If you were on the top oor of one of the Petronas Towers in Malaysia at a height of 370 meters, what would be the distance from your eye to the horizon?
2. If you were in a hot air balloon oating at a height of 1,000 meters, what would be the distance from your eye to the horizon?
3. If you were at a height of meters above Earth’s surface, what would be the distance from your eye to the horizon?
4. The International Space Station is 408,773 meters above Earth’s surface. If you were an astronaut on the ISS, what fraction of Earth’s circumference would you be able to see?
5. If you were on the top oor of one of the Petronas Towers in Malaysia at a height of 370 meters, how far would it be for someone to walk along Earth from the base of the building to your horizon?
Student Response
1. Approximately 68,664 meters. 2. Approximately 112,885 meters.
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Teacher Guide