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Solving Triangle and Distance Problems Using the Pythagorean Theorem

This document presents a series of mathematical problems involving right triangles and distance calculations. It explores the use of the Pythagorean theorem to find the hypotenuse of a triangle given the lengths of the other two sides. Additionally, it covers real-life scenarios, like determining the shortest distance traveled after moving in two perpendicular directions and assessing distances between locations on a map. Each problem comes with multiple-choice answers to enhance understanding and application of geometric concepts.

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Solving Triangle and Distance Problems Using the Pythagorean Theorem

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  1. Aileen is making a flag for one of her classes. The flag is in the shape of a right triangle. If the two sides of the triangle are 5 inches and 12 inches, what is the length of the third side (hypotenuse)?

  2. Cameron walked 9 meters due east and then 40 meters due north in Central Park in New York City. What is the shortest distance from the point where Cameron started to where she ended? A. 31 B. 41 C. 49 D. 360

  3. Jeb built a ramp like the one pictured below. What is the height, in inches, of Jeb’s ramp? A. 5 B. 12 C. 18 D. 36 13 in. height 12 in.

  4. Lookout Road is perpendicular to Village Road. Sam knows that the straight-line distance from his house to Julie’s house is 15 miles. Julie knows that the straight-line distance from her house to the library is 12 miles. Sam used the Pythagorean Theorem to estimate the distance from his house to the library. What is the distance from Sam’s house to the library? A. 3 miles B. 9 miles C. 12 miles D. 27 miles

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