Learners practice relating rules of trigonometry and properties of circles. With a few simplifying assumptions such as a perfectly round earth, young mathematicians calculate the lengths of various paths between satellite and stations. In a classroom where students likely consider their cell phone as an extension of themselves, finding the many thousands of miles a signal must travel could certainly be surprising.

Concepts

circles, tangent, right triangles, arc length, law of cosines, trigonometric, ratios

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Additional Tags

math

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Instructional Ideas

• Could be a problem set introduction to a real-life geometry project (calculating dimensions in application)
• Good open-response practice question for end of course testing
• Could be done in conjunction with a science lesson on satellites or cell phone signals for a cross-curriculum unit

Classroom Considerations

• Higher reading level introduction might require ESL support
• Assumes learners already know how to use Pythagorean's theorem, calculate arc length, use trigonometric ratios, and apply the law of cosines
• First page worksheet for students has no room for recording answers and calculations 

Pros

• Challenging but not overwhelming constraints
• Clearly worked out step-by-step solutions
• Hints for helping learners avoid common pitfalls

Cons

• None

Common Core

HSG-MG.A.3 MP4