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# M8.4.2

Understands the characteristics and uses of basic trigonometric functions.

### How Big Is the Earth?

In collaboration with another school north or south of yours, rnuse the method of Eratoshenes to determine the circumference rnof the Earth.

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### Pilots, Airplanes, and the Tangent of Three (3) Degrees

When approaching an airport, pilots must learn to maneuver their aircraft visually, so that a stabilized approach to the runway can be flown at a constant approach angle. Precise approach planning insures a smooth transition to a landing within the Touchdown Zone (1) of the runway. Pilots must sometimes execute visual approaches that are varied in size, shape, and angle based upon a variety of factors such as: other aircraft, obstructions, noise abatement, or prevailing weather conditions. The standard approach angle however, is 3&deg;.

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### How Far Can You See?

Problem: Fire towers are built so firefighters in forested regions can scan large areas for potential trouble. Upper-story and penthouse apartments rent for the highest prices because of the terrific views. Assuming the atmosphere is clear, and there are no hills or mountains obstructing the view, how far could you see to the horizon from the top of a 100 meter fire tower? From the top of a 55 story skyscraper, where each floor is 3 meters high? From the top of the tallest building in the world (the Petronis Tower in Kuala Lumpur, Malaysia, 1,467 ft. high)?

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### Determining the Altitude of Iridium Flares

If you have a clear night and you're somewhat removed from city lights, many satellites are fairly easy objects to see. They look like faint stars (occasionally bright stars) gliding across the night sky. Sometimes satellites look like airplanes, but airplanes have blinking lights that are usually colored. What's interesting about Iridium satellites, from a star gazing point of view, is that they can suddenly brighten and may easily outshine every star or planet in the sky.

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