Final answer:
Thales calculated the height of the Great Pyramid of Cheops using similar triangles formed by shadows. By comparing the shadow of a 3 ft pole to the 586 ft shadow of the pyramid, the calculated height is found to be 293 ft to the nearest foot.
Step-by-step explanation:
The ancient Greek mathematician Thales reportedly calculated the height of the Great Pyramid of Cheops by using the proportions of the shadows cast by the pyramid and a separate pole. According to the question, Thales used a 3 ft pole that cast a 6 ft shadow, and he noted that the pyramid's shadow was 586 ft long.
To find the height of the pyramid, we use the concept of similar triangles.
The ratios of heights to shadows for the pole and the pyramid should be the same because the sun's rays are parallel. This can be represented by the equation:
Height of pole / Shadow of pole = Height of pyramid / Shadow of pyramid
Plugging in the values we have:
3 ft / 6 ft = Height of pyramid / 586 ft
From this proportion, we can solve for the height of the pyramid:
Height of pyramid = (3 ft / 6 ft) × 586 ft = 1/2 × 586 ft = 293 ft
Therefore, the height of the pyramid is 293 ft, to the nearest foot.