Question

How Tall Is the Great Pyramid? The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He measured the length of the pyramid's shadow to be 114 paces and determined the length of his shadow to be 3 paces. See the illustration. Using similar triangles, determine the height of the Great Pyramid in terms of the number of paces.

Name: Problem 53, Chapter 0: College Algebra
Uploaded: 2020-03-08T00:16:22-08:00
Duration: 2 min 36 s
Channel: Kerri Mccallon

   How Tall Is the Great Pyramid? The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He measured the length of the pyramid's shadow to be 114 paces and determined the length of his shadow to be 3 paces. See the illustration. Using similar triangles, determine the height of the Great Pyramid in terms of the number of paces.

College Algebra

Michael Sullivan 10th Edition

Chapter 0, Problem 53

Instant Answer

Solved by Expert Kerri Mccallon

03/08/2020

Step 1

One is formed by Thales and his shadow, and the other is formed by the pyramid and its shadow. We know that the ratio of corresponding sides in similar triangles is equal. Therefore, we can set up the following proportion: \[ \frac{{\text{{Height of Show more…

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How Tall Is the Great Pyramid? The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He measured the length of the pyramid's shadow to be 114 paces and determined the length of his shadow to be 3 paces. See the illustration. Using similar triangles, determine the height of the Great Pyramid in terms of the number of paces.

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Key Concepts

Proportionality

Proportionality in geometry means that the ratios between corresponding sides of similar figures are the same. This relationship makes it possible to solve for unknown measurements by comparing them to measured lengths.

Shadow Reckoning

Shadow reckoning is an ancient method of measurement that uses the lengths of shadows cast by objects along with the principles of similar triangles. By comparing the ratios of known heights to their shadows, one can accurately determine the height of an object even without direct measurement.

Similar Triangles

This concept involves triangles that have identical angles and therefore proportional corresponding sides. It allows one to scale figures and determine unknown lengths by setting up proportional relationships between known dimensions.

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