Pythagorean Theorem

Geometry Tutorial

Pythagorean Theorem


In this problem, the student will be give two distances as two sides of a triangle, and will need to use the Pythagorean Theorem to calculate how far a woman lives from her workplace. The Pythagorean Theorem is a formula used to determine the length of one side of a triangle if two of the other sides are known, and is shown as “a^2 + b^2 = c^2” with “a” and “b” being the sides of the triangle, and “c” being the hypotenuse.

Sample Problem

Angela drives her car to work each morning from her apartment. She first drives east 4.6 miles and then north 7.3 miles to arrive at work. How far does she live from her workplace if she were able to walk directly there?


1. Draw a rough diagram of the problem, and label the lengths of each side.
2. Draw the hypotenuse as the direct distance Angela lives from work.
3. Plug in the numbers into the Pythagorean Theorem and calculate “c^2”. (a = 4.6, b = 7.3; 4.6^2 + 7.3^2 = c^2)
4. c^2 = 74.45. Because we want to find “c” by itself, take the square root of “c^2”.
5. The square root of 74.45 = 8.62844… round to the nearest tenth decimal place, 8.6. So “c” = 8.6.
6. Therefore, the distance that Angela lives directly from work is 8.6 miles.

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I am currently a Senior at the University of Nebraska – Kearney, studying Exercise Science with minors in Nutrition and Chemistry. I am in the Honors Program on Campus and am currently engaging in Undergraduate Research in the Kinesiology and Sports Sciences department. I have always enjoyed learn...
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