Final answer:
The slope of each triangular face of the Pyramid of the Feathered Serpent in Teotihuacan, which has a square base, is approximately 0.597. This is calculated using Pythagoras' theorem to find the slant height and then dividing the height of the pyramid by half the length of the base.
Step-by-step explanation:
The student asked about the slope of each triangular face of a pyramid with a square base situated in Teotihuacan, Mexico, specifically referring to the Pyramid of the Feathered Serpent. The information given is the distance from the center of the base to the center of an edge (32.5m) and the height of the pyramid (19.4m).
To find the slope of the triangular face, we need to determine the length of the slant height (l) of the pyramid. The slant height forms the hypotenuse of a right-angled triangle where half the length of the base (b/2) and the height (h) of the pyramid are the other two sides. The length of the base can be found by multiplying the given center-to-edge distance by 2, hence b = 2 × 32.5m = 65m.
Using Pythagoras' theorem, we calculate the slant height (l):
l² = (b/2)² + h²
l² = (65/2)² + 19.4²
l² = 32.5² + 19.4²
l² = 1056.25 + 376.36
l = sqrt(1432.61)
l ≈ 37.85m
The slope of the triangular face is defined as the change in height over the change in base, or the rise over the run. Therefore, the slope (m) equals the height (h) divided by half the length of the base (b/2):
m = h / (b/2)
m = 19.4 / (65/2)
m = 19.4 / 32.5
m ≈ 0.597