Chapter A.2, Problem 51AYU

To determine

To find: The height of the Great Pyramid in terms of the number of paces.

Answer to Problem 51AYU

160

Explanation of Solution

Given:

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.

Calculation:

By the similar triangle theorem, which states that a triangle with the same angles has proportionate sides.

Here Pyramid and Man standing in the same angle, therefore the shadow length and height are proportional.

In other words, the sides of similar triangles are proportionate so their ratios will be equal.

$\frac{3}{2}=\frac{240}{x}$

$x=\frac{240\times 2}{3}=160$