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Tethys, Calypso, and Telesto are three of Saturn’s moons, each with a nearly circular orbit at a radius of 295,000 kilometers. The Cassini-Huygens spacecraft has been exploring Saturn since July 2004. Telesto orbits at a point of tangency, and using geometric principles, we can calculate the distance from Cassini to Tethys. Using Theorem 10.16, we find the distance DB from Cassini to Tethys approximated to 496,494 kilometers. This problem-solving approach illustrates the application of mathematics in real-world scenarios.
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Tethys, Calypso, and Telesto are three of Saturn’s moons. Each has a nearly circular orbit 295,000 kilometers in radius. The Cassini-Huygens spacecraft entered Saturn’s orbit in July 2004. Telesto is on a point of tangency. Find the distance DB from Cassini to Tethys. EXAMPLE 4 Solve a real-world problem SCIENCE
DC DB = AD2 83,000 DB 203,0002 DB 496,494 ANSWER Cassini is about 496,494 kilometers from Tethys. EXAMPLE 4 Solve a real-world problem SOLUTION Use Theorem 10.16. Substitute. Solve for DB.
ANSWER Since the distances given are not exact, it is appropriate to use the approximation symbol in the solution. for Examples 4 GUIDED PRACTICE 11. Why is it appropriate to use the approximation symbol in the last two steps of the solution to Example 4?
