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Calculating Hypotenuses and Geometry in Real-World Applications

This document covers essential geometry concepts using real-world scenarios. It explores a right triangle with leg lengths of 6 and 8, and calculates the hypotenuse. Additionally, it identifies a triangle with sides 5, 3, and 4 as a right triangle and determines its hypotenuse. Furthermore, it investigates how far a person can see from the Taipei 101 observation deck, 1437 feet above ground, using Earth's radius of 3960 miles. Lastly, it calculates the copper required for a semicircular ornament on a triangle, given specific dimensions.

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Calculating Hypotenuses and Geometry in Real-World Applications

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  1. Section R.3 Geometry Essentials

  2. OBJECTIVE 1

  3. In a right triangle, one leg has a length 6 and the other has length 8. What is the length of the hypotenuse?

  4. Show that a triangle whose sides are of lengths 5, 3, and 4 is a right triangle. Identify the hypotenuse.

  5. Excluding antenna, the tallest inhabited building in the world is Taipei 101 in Taipei, Taiwan. If the indoor observation deck is 1437 feet above ground level, how far can a person standing on the observation deck see (with the aid of a telescope)? Use 3960 miles for the radius of Earth.

  6. OBJECTIVE 2

  7. A Christmas tree ornament is in the shape of a semicircle on top of a triangle. How many square centimeters of copper is required to make the ornament if the height of the triangle is 5 cm and the base is 3 cm?

  8. OBJECTIVE 3

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